Pub Date : 2024-10-24DOI: 10.1016/j.jmaa.2024.128989
Yu Liu, Xiaojun Huang
We generalize Fathi's results by showing that a compact metrizable space admits an fiber expansive homeomorphism if and only if it has a compatible hyperbolic metric. Moreover, we prove that a compact metrizable space admits an fiber expansive homeomorphism if and only if it has a generator in detail. Furthermore, we show that a fiber expansive homeomorphism has finite fiber topological entropy. Finally, we show that fiber Lyapunov exponents for a fiber expansive system are different from zero, indicating that the system presents a chaotic system. Meanwhile, we also prove that negative fiber Lyapunov exponents for compact invariant sets of a dynamical system imply that the compact set is a fiber attractor.
{"title":"Expansiveness, generators and Lyapunov exponents for random bundle transformations","authors":"Yu Liu, Xiaojun Huang","doi":"10.1016/j.jmaa.2024.128989","DOIUrl":"10.1016/j.jmaa.2024.128989","url":null,"abstract":"<div><div>We generalize Fathi's results by showing that a compact metrizable space admits an fiber expansive homeomorphism if and only if it has a compatible hyperbolic metric. Moreover, we prove that a compact metrizable space admits an fiber expansive homeomorphism if and only if it has a generator in detail. Furthermore, we show that a fiber expansive homeomorphism has finite fiber topological entropy. Finally, we show that fiber Lyapunov exponents for a fiber expansive system are different from zero, indicating that the system presents a chaotic system. Meanwhile, we also prove that negative fiber Lyapunov exponents for compact invariant sets of a dynamical system imply that the compact set is a fiber attractor.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"543 2","pages":"Article 128989"},"PeriodicalIF":1.2,"publicationDate":"2024-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142561118","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-24DOI: 10.1016/j.jmaa.2024.128993
Christian Cortés-García
In this paper we propose a mathematical Leslie-Gower predator-prey model, in which the prey takes refuge from the predator when its population size is below a critical threshold, the functional response of the predator is represented by a Holling II function, and the growth of the prey in the absence of the predator is subject to a semi-saturation parameter that affects its birth curve. Since the model is composed of two vector fields, its qualitative analysis includes, in addition to the determination of the number and stability of the equilibria for each vector field and belonging to the biological sense set, the study of the dynamics in the trajectories close to the dividing curve of the two vector fields in order to determine possible pseudo-equilibria. As a result, if the proposed model has a single inner equilibrium, then there is the possibility of having between one or at least two limit cycles, coexisting or not in both vector fields and around the inner equilibrium. Likewise, the model has a stable pseudo-equilibrium which may be surrounded by at least two limit cycle.
在本文中，我们提出了一个莱斯利-高尔捕食者-猎物数学模型，在该模型中，当猎物的种群数量低于临界阈值时，猎物会躲避捕食者，捕食者的功能响应由霍林 II 函数表示，而猎物在没有捕食者的情况下的生长受一个影响其出生曲线的半饱和参数的制约。由于该模型由两个矢量场组成，其定性分析除了确定每个矢量场的平衡点数量和稳定性以及属于生物意义集之外，还包括研究两个矢量场分界曲线附近轨迹的动态，以确定可能的伪平衡点。因此，如果所提出的模型有一个单一的内部平衡，那么在两个矢量场和内部平衡周围就有可能存在一个或至少两个极限循环。同样，该模型也有一个稳定的伪平衡，其周围可能存在至少两个极限循环。
{"title":"Population dynamics in a Leslie-Gower predator-prey model with proportional prey refuge at low densities","authors":"Christian Cortés-García","doi":"10.1016/j.jmaa.2024.128993","DOIUrl":"10.1016/j.jmaa.2024.128993","url":null,"abstract":"<div><div>In this paper we propose a mathematical Leslie-Gower predator-prey model, in which the prey takes refuge from the predator when its population size is below a critical threshold, the functional response of the predator is represented by a Holling II function, and the growth of the prey in the absence of the predator is subject to a semi-saturation parameter that affects its birth curve. Since the model is composed of two vector fields, its qualitative analysis includes, in addition to the determination of the number and stability of the equilibria for each vector field and belonging to the biological sense set, the study of the dynamics in the trajectories close to the dividing curve of the two vector fields in order to determine possible pseudo-equilibria. As a result, if the proposed model has a single inner equilibrium, then there is the possibility of having between one or at least two limit cycles, coexisting or not in both vector fields and around the inner equilibrium. Likewise, the model has a stable pseudo-equilibrium which may be surrounded by at least two limit cycle.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"543 2","pages":"Article 128993"},"PeriodicalIF":1.2,"publicationDate":"2024-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142561121","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-23DOI: 10.1016/j.jmaa.2024.128990
Gui-Chun Jiang , Yu-Ying Wang , Gao-Feng Zheng
<div><div>In this paper, we are concerned with the following initial-boundary value problem<span><span><span><math><mrow><mo>{</mo><mtable><mtr><mtd><msub><mrow><mi>u</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>=</mo><mi>Δ</mi><mi>u</mi><mo>+</mo><mi>Q</mi><mo>(</mo><mo>|</mo><mi>x</mi><mo>|</mo><mo>)</mo><mo>|</mo><mi>u</mi><msup><mrow><mo>|</mo></mrow><mrow><mi>p</mi><mo>−</mo><mn>1</mn></mrow></msup><mi>u</mi><mo>,</mo></mtd><mtd><mi>x</mi><mo>∈</mo><msub><mrow><mi>B</mi></mrow><mrow><mi>R</mi></mrow></msub><mo>,</mo><mi>t</mi><mo>></mo><mn>0</mn></mtd></mtr><mtr><mtd><mi>u</mi><mo>(</mo><mi>x</mi><mo>,</mo><mi>t</mi><mo>)</mo><mo>=</mo><mn>0</mn><mo>,</mo></mtd><mtd><mi>x</mi><mo>∈</mo><mo>∂</mo><msub><mrow><mi>B</mi></mrow><mrow><mi>R</mi></mrow></msub><mo>,</mo><mi>t</mi><mo>></mo><mn>0</mn></mtd></mtr><mtr><mtd><mi>u</mi><mo>(</mo><mi>x</mi><mo>,</mo><mn>0</mn><mo>)</mo><mo>=</mo><msub><mrow><mi>u</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>(</mo><mi>x</mi><mo>)</mo><mo>,</mo></mtd><mtd><mi>x</mi><mo>∈</mo><msub><mrow><mi>B</mi></mrow><mrow><mi>R</mi></mrow></msub><mo>,</mo></mtd></mtr></mtable></mrow></math></span></span></span> where <span><math><mi>p</mi><mo>≥</mo><msub><mrow><mi>p</mi></mrow><mrow><mi>s</mi></mrow></msub><mo>:</mo><mo>=</mo><mfrac><mrow><mi>N</mi><mo>+</mo><mn>2</mn></mrow><mrow><mi>N</mi><mo>−</mo><mn>2</mn></mrow></mfrac></math></span>, <span><math><msub><mrow><mi>u</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>∈</mo><msup><mrow><mi>L</mi></mrow><mrow><mo>∞</mo></mrow></msup><mo>(</mo><msub><mrow><mi>B</mi></mrow><mrow><mi>R</mi></mrow></msub><mo>)</mo></math></span>, and <span><math><mi>Q</mi><mo>(</mo><mi>r</mi><mo>)</mo><mo>∈</mo><msup><mrow><mi>C</mi></mrow><mrow><mn>1</mn></mrow></msup><mo>(</mo><mo>[</mo><mn>0</mn><mo>,</mo><mi>R</mi><mo>]</mo><mo>)</mo></math></span>, <span><math><mn>0</mn><mo><</mo><munder><mrow><mi>C</mi></mrow><mo>_</mo></munder><mo>≤</mo><mi>Q</mi><mo>(</mo><mi>r</mi><mo>)</mo><mo>≤</mo><mover><mrow><mi>C</mi></mrow><mo>‾</mo></mover><mo><</mo><mo>∞</mo><mo>,</mo><mspace></mspace><msup><mrow><mi>Q</mi></mrow><mrow><mo>′</mo></mrow></msup><mo>(</mo><mi>r</mi><mo>)</mo><mo>≤</mo><mn>0</mn></math></span>. We extend the asymptotic behavior results, which is well-known when <em>Q</em> is constant according to Matano-Merle (cf. <span><span>[25]</span></span>), for the blow-up solutions. More precisely, we show that when <span><math><msub><mrow><mi>p</mi></mrow><mrow><mi>s</mi></mrow></msub><mo>≤</mo><mi>p</mi><mo><</mo><msup><mrow><mi>p</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span>, the blowup of radial solution to this problem is always of Type I. This result partially generalizes the conclusions in <span><span>[25]</span></span> for <span><math><mi>Q</mi><mo>≡</mo><mn>1</mn></math></span>. This extension is nontrivial due to the appearance of <em>Q</em>. The quasi-monotonicity formula established by the third author and Cheng in <span><span>[8]</span></span> allows us
{"title":"On type I blowup of some nonlinear heat equations with a potential","authors":"Gui-Chun Jiang , Yu-Ying Wang , Gao-Feng Zheng","doi":"10.1016/j.jmaa.2024.128990","DOIUrl":"10.1016/j.jmaa.2024.128990","url":null,"abstract":"<div><div>In this paper, we are concerned with the following initial-boundary value problem<span><span><span><math><mrow><mo>{</mo><mtable><mtr><mtd><msub><mrow><mi>u</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>=</mo><mi>Δ</mi><mi>u</mi><mo>+</mo><mi>Q</mi><mo>(</mo><mo>|</mo><mi>x</mi><mo>|</mo><mo>)</mo><mo>|</mo><mi>u</mi><msup><mrow><mo>|</mo></mrow><mrow><mi>p</mi><mo>−</mo><mn>1</mn></mrow></msup><mi>u</mi><mo>,</mo></mtd><mtd><mi>x</mi><mo>∈</mo><msub><mrow><mi>B</mi></mrow><mrow><mi>R</mi></mrow></msub><mo>,</mo><mi>t</mi><mo>></mo><mn>0</mn></mtd></mtr><mtr><mtd><mi>u</mi><mo>(</mo><mi>x</mi><mo>,</mo><mi>t</mi><mo>)</mo><mo>=</mo><mn>0</mn><mo>,</mo></mtd><mtd><mi>x</mi><mo>∈</mo><mo>∂</mo><msub><mrow><mi>B</mi></mrow><mrow><mi>R</mi></mrow></msub><mo>,</mo><mi>t</mi><mo>></mo><mn>0</mn></mtd></mtr><mtr><mtd><mi>u</mi><mo>(</mo><mi>x</mi><mo>,</mo><mn>0</mn><mo>)</mo><mo>=</mo><msub><mrow><mi>u</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>(</mo><mi>x</mi><mo>)</mo><mo>,</mo></mtd><mtd><mi>x</mi><mo>∈</mo><msub><mrow><mi>B</mi></mrow><mrow><mi>R</mi></mrow></msub><mo>,</mo></mtd></mtr></mtable></mrow></math></span></span></span> where <span><math><mi>p</mi><mo>≥</mo><msub><mrow><mi>p</mi></mrow><mrow><mi>s</mi></mrow></msub><mo>:</mo><mo>=</mo><mfrac><mrow><mi>N</mi><mo>+</mo><mn>2</mn></mrow><mrow><mi>N</mi><mo>−</mo><mn>2</mn></mrow></mfrac></math></span>, <span><math><msub><mrow><mi>u</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>∈</mo><msup><mrow><mi>L</mi></mrow><mrow><mo>∞</mo></mrow></msup><mo>(</mo><msub><mrow><mi>B</mi></mrow><mrow><mi>R</mi></mrow></msub><mo>)</mo></math></span>, and <span><math><mi>Q</mi><mo>(</mo><mi>r</mi><mo>)</mo><mo>∈</mo><msup><mrow><mi>C</mi></mrow><mrow><mn>1</mn></mrow></msup><mo>(</mo><mo>[</mo><mn>0</mn><mo>,</mo><mi>R</mi><mo>]</mo><mo>)</mo></math></span>, <span><math><mn>0</mn><mo><</mo><munder><mrow><mi>C</mi></mrow><mo>_</mo></munder><mo>≤</mo><mi>Q</mi><mo>(</mo><mi>r</mi><mo>)</mo><mo>≤</mo><mover><mrow><mi>C</mi></mrow><mo>‾</mo></mover><mo><</mo><mo>∞</mo><mo>,</mo><mspace></mspace><msup><mrow><mi>Q</mi></mrow><mrow><mo>′</mo></mrow></msup><mo>(</mo><mi>r</mi><mo>)</mo><mo>≤</mo><mn>0</mn></math></span>. We extend the asymptotic behavior results, which is well-known when <em>Q</em> is constant according to Matano-Merle (cf. <span><span>[25]</span></span>), for the blow-up solutions. More precisely, we show that when <span><math><msub><mrow><mi>p</mi></mrow><mrow><mi>s</mi></mrow></msub><mo>≤</mo><mi>p</mi><mo><</mo><msup><mrow><mi>p</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span>, the blowup of radial solution to this problem is always of Type I. This result partially generalizes the conclusions in <span><span>[25]</span></span> for <span><math><mi>Q</mi><mo>≡</mo><mn>1</mn></math></span>. This extension is nontrivial due to the appearance of <em>Q</em>. The quasi-monotonicity formula established by the third author and Cheng in <span><span>[8]</span></span> allows us","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"543 2","pages":"Article 128990"},"PeriodicalIF":1.2,"publicationDate":"2024-10-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142554628","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-23DOI: 10.1016/j.jmaa.2024.128991
Tomoyuki Nakatsuka
In this paper, the existence of time-periodic strong solutions to the Navier-Stokes equation in is established under a suitable smallness condition on the external force. Our analysis is based on splitting periodic solutions into steady and purely periodic parts. One advantage of this decomposition is the availability of slightly more regularity in time of the purely periodic part. We apply this property to construct time-periodic solutions of the Navier-Stokes equation with information on the classes of their steady and purely periodic parts. It is also shown that the small solution v constructed in our existence theorem is unique within a class of time-periodic, not necessarily small, solutions having the same integrability properties as v.
本文在外力的适当小度条件下，建立了 Rn 中纳维-斯托克斯方程的时间周期强解的存在性。我们的分析基于将周期解分割为稳定部分和纯周期部分。这种分解方法的一个优点是纯周期部分在时间上的规律性稍强。我们将这一特性应用于构建 Navier-Stokes 方程的时间周期解，并提供其稳定部分和纯周期部分的类别信息。我们还证明，在我们的存在定理中构建的小解 v 在一类时间周期解（不一定是小解）中是唯一的，该类解具有与 v 相同的可积分性。
{"title":"Existence of time-periodic strong solutions to the Navier-Stokes equation in the whole space","authors":"Tomoyuki Nakatsuka","doi":"10.1016/j.jmaa.2024.128991","DOIUrl":"10.1016/j.jmaa.2024.128991","url":null,"abstract":"<div><div>In this paper, the existence of time-periodic strong solutions to the Navier-Stokes equation in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span> is established under a suitable smallness condition on the external force. Our analysis is based on splitting periodic solutions into steady and purely periodic parts. One advantage of this decomposition is the availability of slightly more regularity in time of the purely periodic part. We apply this property to construct time-periodic solutions of the Navier-Stokes equation with information on the classes of their steady and purely periodic parts. It is also shown that the small solution <em>v</em> constructed in our existence theorem is unique within a class of time-periodic, not necessarily small, solutions having the same integrability properties as <em>v</em>.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"543 2","pages":"Article 128991"},"PeriodicalIF":1.2,"publicationDate":"2024-10-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142554630","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-23DOI: 10.1016/j.jmaa.2024.128985
X. Carvajal , P. Gamboa , R. Santos
We consider the initial value problem (IVP) associated with a higher order non-linear Schrödinger (h-NLS) equation with given data in the modulation space . Using ideas from Killip, Visan, Zhang, Oh and Wang, we prove that the IVP associated with the h-NLS equation is globally well-posed in the modulation spaces for and .
{"title":"Global well-posedness for the higher order non-linear Schrödinger equation in modulation spaces","authors":"X. Carvajal , P. Gamboa , R. Santos","doi":"10.1016/j.jmaa.2024.128985","DOIUrl":"10.1016/j.jmaa.2024.128985","url":null,"abstract":"<div><div>We consider the initial value problem (IVP) associated with a higher order non-linear Schrödinger (h-NLS) equation<span><span><span><math><msub><mrow><mo>∂</mo></mrow><mrow><mi>t</mi></mrow></msub><mi>u</mi><mo>+</mo><mi>i</mi><mi>a</mi><msubsup><mrow><mo>∂</mo></mrow><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msubsup><mi>u</mi><mo>+</mo><mi>b</mi><msubsup><mrow><mo>∂</mo></mrow><mrow><mi>x</mi></mrow><mrow><mn>3</mn></mrow></msubsup><mi>u</mi><mo>=</mo><mn>2</mn><mi>i</mi><mi>a</mi><mo>|</mo><mi>u</mi><msup><mrow><mo>|</mo></mrow><mrow><mn>2</mn></mrow></msup><mi>u</mi><mo>+</mo><mn>6</mn><mi>b</mi><mo>|</mo><mi>u</mi><msup><mrow><mo>|</mo></mrow><mrow><mn>2</mn></mrow></msup><msub><mrow><mo>∂</mo></mrow><mrow><mi>x</mi></mrow></msub><mi>u</mi><mo>,</mo><mspace></mspace><mi>x</mi><mo>,</mo><mi>t</mi><mo>∈</mo><mi>R</mi><mo>,</mo></math></span></span></span> with given data in the modulation space <span><math><msubsup><mrow><mi>M</mi></mrow><mrow><mi>s</mi></mrow><mrow><mn>2</mn><mo>,</mo><mi>p</mi></mrow></msubsup><mo>(</mo><mi>R</mi><mo>)</mo></math></span>. Using ideas from Killip, Visan, Zhang, Oh and Wang, we prove that the IVP associated with the h-NLS equation is globally well-posed in the modulation spaces <span><math><msubsup><mrow><mi>M</mi></mrow><mrow><mi>s</mi></mrow><mrow><mn>2</mn><mo>,</mo><mi>p</mi></mrow></msubsup><mo>(</mo><mi>R</mi><mo>)</mo></math></span> for <span><math><mi>s</mi><mo>≥</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>4</mn></mrow></mfrac></math></span> and <span><math><mi>p</mi><mo>≥</mo><mn>2</mn></math></span>.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"543 2","pages":"Article 128985"},"PeriodicalIF":1.2,"publicationDate":"2024-10-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142552289","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-23DOI: 10.1016/j.jmaa.2024.128986
Ivan Gudoshnikov, Michal Křížek
We revisit stress problems in linear elasticity to provide a perspective from the geometrical and functional-analytic points of view. For the static stress problem of linear elasticity with mixed boundary conditions we present the associated pair of unbounded adjoint operators. Such a pair is explicitly written for the first time, despite the abundance of the literature on the topic. We use it to find the stress solution as an intersection of the (affinely translated) fundamental subspaces of the adjoint operators. In particular, we treat the equilibrium equation in the operator form, which involves the spaces of traces on a part of the boundary, known as the Lions-Magenes spaces. Our analysis of the pair of adjoint operators for the problem with mixed boundary conditions relies on the properties of the analogous pair of operators for the problem with the displacement boundary conditions, which we also include in the paper.
{"title":"Stress solution of static linear elasticity with mixed boundary conditions via adjoint linear operators","authors":"Ivan Gudoshnikov, Michal Křížek","doi":"10.1016/j.jmaa.2024.128986","DOIUrl":"10.1016/j.jmaa.2024.128986","url":null,"abstract":"<div><div>We revisit stress problems in linear elasticity to provide a perspective from the geometrical and functional-analytic points of view. For the static stress problem of linear elasticity with mixed boundary conditions we present the associated pair of unbounded adjoint operators. Such a pair is explicitly written for the first time, despite the abundance of the literature on the topic. We use it to find the stress solution as an intersection of the (affinely translated) fundamental subspaces of the adjoint operators. In particular, we treat the equilibrium equation in the operator form, which involves the spaces of traces on a part of the boundary, known as the Lions-Magenes spaces. Our analysis of the pair of adjoint operators for the problem with mixed boundary conditions relies on the properties of the analogous pair of operators for the problem with the displacement boundary conditions, which we also include in the paper.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"543 2","pages":"Article 128986"},"PeriodicalIF":1.2,"publicationDate":"2024-10-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142554629","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-22DOI: 10.1016/j.jmaa.2024.128992
Luis Acuña Valverde
In this paper, we study the heat content for the Schrödinger operator related to a subordinate Brownian motion and we also establish its small time asymptotic behavior for suitable potentials V. The case for and Ω a Borel set of finite measure is investigated in detail.
本文研究了与隶属布朗运动有关的薛定谔算子的热含量，并确定了其在合适的势 V 下的小时间渐近行为。
{"title":"Estimates concerning the heat content for the Schrödinger operator related to a subordinate Brownian motion","authors":"Luis Acuña Valverde","doi":"10.1016/j.jmaa.2024.128992","DOIUrl":"10.1016/j.jmaa.2024.128992","url":null,"abstract":"<div><div>In this paper, we study the heat content for the Schrödinger operator related to a subordinate Brownian motion and we also establish its small time asymptotic behavior for suitable potentials <em>V</em>. The case <span><math><mi>V</mi><mo>=</mo><mi>c</mi><msub><mrow><mn>1</mn></mrow><mrow><mi>Ω</mi></mrow></msub></math></span> for <span><math><mi>c</mi><mo>></mo><mn>0</mn></math></span> and Ω a Borel set of finite measure is investigated in detail.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"543 2","pages":"Article 128992"},"PeriodicalIF":1.2,"publicationDate":"2024-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142554627","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-22DOI: 10.1016/j.jmaa.2024.128978
C. Bellavita , V. Daskalogiannis , G. Nikolaidis , G. Stylogiannis
For g in BMOA, we consider the generalized Volterra operator acting on Hardy spaces . This article aims to study the largest space of analytic functions, which is mapped by into the Hardy space . We call this space the optimal domain of and we describe its structural properties. Motivation for this comes from the work of G. Curbera and W. Ricker [7] who studied the optimal domain of the classical Cesáro operator.
对于 BMOA 中的 g，我们考虑作用于 Hardy 空间 Hp 的广义 Volterra 算子 Tg。本文旨在研究由 Tg 映射到哈代空间 Hp 的最大解析函数空间。我们称这个空间为 Tg 的最优域，并描述其结构特性。本文的研究动机来自 G. Curbera 和 W. Ricker [7]的工作，他们研究了经典 Cesáro 算子的最优域。
{"title":"Optimal domain of generalized Volterra operators","authors":"C. Bellavita , V. Daskalogiannis , G. Nikolaidis , G. Stylogiannis","doi":"10.1016/j.jmaa.2024.128978","DOIUrl":"10.1016/j.jmaa.2024.128978","url":null,"abstract":"<div><div>For <em>g</em> in BMOA, we consider the generalized Volterra operator <span><math><msub><mrow><mi>T</mi></mrow><mrow><mi>g</mi></mrow></msub></math></span> acting on Hardy spaces <span><math><msup><mrow><mi>H</mi></mrow><mrow><mi>p</mi></mrow></msup></math></span>. This article aims to study the largest space of analytic functions, which is mapped by <span><math><msub><mrow><mi>T</mi></mrow><mrow><mi>g</mi></mrow></msub></math></span> into the Hardy space <span><math><msup><mrow><mi>H</mi></mrow><mrow><mi>p</mi></mrow></msup></math></span>. We call this space the optimal domain of <span><math><msub><mrow><mi>T</mi></mrow><mrow><mi>g</mi></mrow></msub></math></span> and we describe its structural properties. Motivation for this comes from the work of G. Curbera and W. Ricker <span><span>[7]</span></span> who studied the optimal domain of the classical Cesáro operator.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"543 2","pages":"Article 128978"},"PeriodicalIF":1.2,"publicationDate":"2024-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142527627","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-22DOI: 10.1016/j.jmaa.2024.128988
Zewen Wang , Weili Zhu , Bin Wu , Bin Hu
In this paper, we consider a backward problem in time for a linear stochastic Kuramoto-Sivashinsky equation. Firstly, we present two Carleman estimates incorporating weight functions independent of the variable x for the stochastic Kuramoto-Sivashinsky equation. Subsequently, we employ these two Carleman estimates to establish conditional stability for the backward problem in two distinct scenarios: when and when . Lastly, we transform the backward problem in time into the minimization of a regularized Tikhonov functional. This functional is solved by the conjugate gradient algorithm based on the gradient formula tailored for the regularized functional. Numerical examples related to the recovery of continuous and discontinuous initial values illustrate the effectiveness of the conjugate gradient algorithm.
{"title":"A backward problem for stochastic Kuramoto-Sivashinsky equation: Conditional stability and numerical solution","authors":"Zewen Wang , Weili Zhu , Bin Wu , Bin Hu","doi":"10.1016/j.jmaa.2024.128988","DOIUrl":"10.1016/j.jmaa.2024.128988","url":null,"abstract":"<div><div>In this paper, we consider a backward problem in time for a linear stochastic Kuramoto-Sivashinsky equation. Firstly, we present two Carleman estimates incorporating weight functions independent of the variable <em>x</em> for the stochastic Kuramoto-Sivashinsky equation. Subsequently, we employ these two Carleman estimates to establish conditional stability for the backward problem in two distinct scenarios: when <span><math><mn>0</mn><mo><</mo><msub><mrow><mi>t</mi></mrow><mrow><mn>0</mn></mrow></msub><mo><</mo><mi>T</mi></math></span> and when <span><math><msub><mrow><mi>t</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>=</mo><mn>0</mn></math></span>. Lastly, we transform the backward problem in time into the minimization of a regularized Tikhonov functional. This functional is solved by the conjugate gradient algorithm based on the gradient formula tailored for the regularized functional. Numerical examples related to the recovery of continuous and discontinuous initial values illustrate the effectiveness of the conjugate gradient algorithm.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"543 2","pages":"Article 128988"},"PeriodicalIF":1.2,"publicationDate":"2024-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142560610","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-22DOI: 10.1016/j.jmaa.2024.128979
Xiaojing Zhou
In this paper, we introduce a new class of generalized Möbius function space of analytic functions in the unit disk, that contains , , , and as particular cases. We study several basic properties of such new spaces and also characterize these spaces via Carleson-type measures. As for some applications, we study the corresponding little-o spaces, as well as establish several embedding relations of these new spaces with Bloch-type spaces. Our result generalizes an early work of Zhu in 2007.
{"title":"On a generalized Möbius invariant function space","authors":"Xiaojing Zhou","doi":"10.1016/j.jmaa.2024.128979","DOIUrl":"10.1016/j.jmaa.2024.128979","url":null,"abstract":"<div><div>In this paper, we introduce a new class of generalized Möbius function space of analytic functions in the unit disk, that contains <span><math><msub><mrow><mi>B</mi></mrow><mrow><mi>α</mi></mrow></msub></math></span>, <span><math><msubsup><mrow><mi>B</mi></mrow><mrow><mi>α</mi></mrow><mrow><mi>p</mi></mrow></msubsup></math></span>, <span><math><msubsup><mrow><mtext>BMOA</mtext></mrow><mrow><mi>p</mi></mrow><mrow><mi>α</mi></mrow></msubsup></math></span>, and <span><math><mi>F</mi><mo>(</mo><mi>p</mi><mo>,</mo><mi>p</mi><mi>α</mi><mo>−</mo><mn>2</mn><mo>,</mo><mi>s</mi><mo>)</mo></math></span> as particular cases. We study several basic properties of such new spaces and also characterize these spaces via Carleson-type measures. As for some applications, we study the corresponding little-o spaces, as well as establish several embedding relations of these new spaces with Bloch-type spaces. Our result generalizes an early work of Zhu in 2007.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"543 2","pages":"Article 128979"},"PeriodicalIF":1.2,"publicationDate":"2024-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142527628","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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