Pub Date : 2025-02-20DOI: 10.1016/j.jmaa.2025.129394
Olga S. Rozanova
Spatial dimensions 1 and 4 play an exceptional role for radial solutions of the pressureless Euler-Poisson equations. Namely, for spatial dimensions other than 1 and 4, any nontrivial solution of the Cauchy problem blows up in finite time (except for special cases), whereas for dimensions 1 and 4 there exists a neighborhood of trivial initial data in the -norm such that the corresponding solution preserves the initial smoothness globally. This is explained by the fact that only in these dimensions all Lagrangian trajectories are periodic with the same period. For dimension 1, a criterion for the formation of a singularity in terms of initial data was known, however, for the much more difficult case of dimension 4, there was no such result. In this paper, we fill this gap. We also describe a class of problems to which the technique used here can be extended with minor modifications.
{"title":"Criterion of singularity formation for radial solutions of the pressureless Euler-Poisson equations in exceptional dimension","authors":"Olga S. Rozanova","doi":"10.1016/j.jmaa.2025.129394","DOIUrl":"10.1016/j.jmaa.2025.129394","url":null,"abstract":"<div><div>Spatial dimensions 1 and 4 play an exceptional role for radial solutions of the pressureless Euler-Poisson equations. Namely, for spatial dimensions other than 1 and 4, any nontrivial solution of the Cauchy problem blows up in finite time (except for special cases), whereas for dimensions 1 and 4 there exists a neighborhood of trivial initial data in the <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span>-norm such that the corresponding solution preserves the initial smoothness globally. This is explained by the fact that only in these dimensions all Lagrangian trajectories are periodic with the same period. For dimension 1, a criterion for the formation of a singularity in terms of initial data was known, however, for the much more difficult case of dimension 4, there was no such result. In this paper, we fill this gap. We also describe a class of problems to which the technique used here can be extended with minor modifications.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"548 2","pages":"Article 129394"},"PeriodicalIF":1.2,"publicationDate":"2025-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143474312","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 : 2025-02-18DOI: 10.1016/j.jmaa.2025.129366
Gargi Ghosh
We consider a bounded domain which is a G-space for a finite complex reflection group G. For each one-dimensional representation of the group G, the relative invariant subspace of the weighted Bergman space on Ω is isometrically isomorphic to a weighted Bergman space on the quotient domain . Consequently, formulae involving the weighted Bergman kernels and projections of Ω and are established. As a result, a transformation rule for the weighted Bergman kernels under a proper holomorphic mapping with G as its group of deck transformations is obtained in terms of the character of the sign representation of G. Explicit expressions for the weighted Bergman kernels of several quotient domains (of the form ) have been deduced to demonstrate the merit of the described formulae.
{"title":"The weighted Bergman spaces and complex reflection groups","authors":"Gargi Ghosh","doi":"10.1016/j.jmaa.2025.129366","DOIUrl":"10.1016/j.jmaa.2025.129366","url":null,"abstract":"<div><div>We consider a bounded domain <span><math><mi>Ω</mi><mo>⊆</mo><msup><mrow><mi>C</mi></mrow><mrow><mi>d</mi></mrow></msup></math></span> which is a <em>G</em>-space for a finite complex reflection group <em>G</em>. For each one-dimensional representation of the group <em>G</em>, the relative invariant subspace of the weighted Bergman space on Ω is isometrically isomorphic to a weighted Bergman space on the quotient domain <span><math><mi>Ω</mi><mo>/</mo><mi>G</mi></math></span>. Consequently, formulae involving the weighted Bergman kernels and projections of Ω and <span><math><mi>Ω</mi><mo>/</mo><mi>G</mi></math></span> are established. As a result, a transformation rule for the weighted Bergman kernels under a proper holomorphic mapping with <em>G</em> as its group of deck transformations is obtained in terms of the character of the sign representation of <em>G</em>. Explicit expressions for the weighted Bergman kernels of several quotient domains (of the form <span><math><mi>Ω</mi><mo>/</mo><mi>G</mi></math></span>) have been deduced to demonstrate the merit of the described formulae.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"548 2","pages":"Article 129366"},"PeriodicalIF":1.2,"publicationDate":"2025-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143488997","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 : 2025-02-18DOI: 10.1016/j.jmaa.2025.129389
Divyang G. Bhimani, Rupak K. Dalai
We completely characterize the weighted Lebesgue spaces on the torus and waveguide manifold for which the solutions of the heat equation converge pointwise (as time tends to zero) to the initial data. In the process, we also characterize the weighted Lebesgue spaces for the boundedness of maximal operators on the torus and waveguide manifold, which may be of independent interest.
{"title":"Pointwise convergence for the heat equation on tori Tn and waveguide manifold Tn×Rm","authors":"Divyang G. Bhimani, Rupak K. Dalai","doi":"10.1016/j.jmaa.2025.129389","DOIUrl":"10.1016/j.jmaa.2025.129389","url":null,"abstract":"<div><div>We completely characterize the weighted Lebesgue spaces on the torus <span><math><msup><mrow><mi>T</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span> and waveguide manifold <span><math><msup><mrow><mi>T</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>×</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>m</mi></mrow></msup></math></span> for which the solutions of the heat equation converge pointwise (as time tends to zero) to the initial data. In the process, we also characterize the weighted Lebesgue spaces for the boundedness of maximal operators on the torus and waveguide manifold, which may be of independent interest.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"548 1","pages":"Article 129389"},"PeriodicalIF":1.2,"publicationDate":"2025-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143455128","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}
A class of point processes is introduced, the so-called dynamic contagion processes having different exciting functions. This is a generalization of that of Hawkes processes as well as of Cox processes with Poisson shot-noise intensity. To define this class the cluster form representation is considered in a way such that the intensity function captures both the self-excited and externally excited jumps by using different exciting functions, that allows us to describe different generations of offspring. For this generalized class, we investigate some asymptotic behaviors such as the Law of Large Numbers, the Central Limit Theorem and the Large Deviation Principle. An application associated with risk models is also discussed under the assumption that the dynamics of contagion claims arrivals have different exciting functions.
{"title":"Asymptotic results for dynamic contagion processes with different exciting functions and application to risk models","authors":"Shamiksha Pandey , Dharmaraja Selvamuthu , Paola Tardelli","doi":"10.1016/j.jmaa.2025.129392","DOIUrl":"10.1016/j.jmaa.2025.129392","url":null,"abstract":"<div><div>A class of point processes is introduced, the so-called dynamic contagion processes having different exciting functions. This is a generalization of that of Hawkes processes as well as of Cox processes with Poisson shot-noise intensity. To define this class the cluster form representation is considered in a way such that the intensity function captures both the self-excited and externally excited jumps by using different exciting functions, that allows us to describe different generations of offspring. For this generalized class, we investigate some asymptotic behaviors such as the Law of Large Numbers, the Central Limit Theorem and the Large Deviation Principle. An application associated with risk models is also discussed under the assumption that the dynamics of contagion claims arrivals have different exciting functions.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"547 2","pages":"Article 129392"},"PeriodicalIF":1.2,"publicationDate":"2025-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143453253","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-02-18DOI: 10.1016/j.jmaa.2025.129385
Jinjun Li, Zhiyi Wu
The Sierpiński type measures are an important class of self-affine measures studied by specialists in geometric measure theory, dynamical systems and probability. In this paper, we investigate the structure of the spectra for the Sierpiński type spectral measure . We first give a sufficient and necessary condition for the family of exponential functions to be a maximal orthogonal set in . Based on this result, we construct a class of regular spectra of . Furthermore, we analyze the Beurling dimensions of the spectra and obtain the optimal upper bound of Beurling dimensions of all spectra, which is in stark contrast with the case of self-similar spectral measures. As an application of our results, we obtain an intermediate property about the Beurling dimension of the spectra.
{"title":"Spectra of the Sierpiński type spectral measure and their Beurling dimensions","authors":"Jinjun Li, Zhiyi Wu","doi":"10.1016/j.jmaa.2025.129385","DOIUrl":"10.1016/j.jmaa.2025.129385","url":null,"abstract":"<div><div>The Sierpiński type measures are an important class of self-affine measures studied by specialists in geometric measure theory, dynamical systems and probability. In this paper, we investigate the structure of the spectra for the Sierpiński type spectral measure <span><math><msub><mrow><mi>μ</mi></mrow><mrow><mi>A</mi><mo>,</mo><mi>D</mi></mrow></msub></math></span>. We first give a sufficient and necessary condition for the family of exponential functions <span><math><mo>{</mo><msup><mrow><mi>e</mi></mrow><mrow><mo>−</mo><mn>2</mn><mi>π</mi><mi>i</mi><mo>〈</mo><mi>λ</mi><mo>,</mo><mi>x</mi><mo>〉</mo></mrow></msup><mo>:</mo><mi>λ</mi><mo>∈</mo><mi>Λ</mi><mo>}</mo></math></span> to be a maximal orthogonal set in <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>(</mo><msub><mrow><mi>μ</mi></mrow><mrow><mi>A</mi><mo>,</mo><mi>D</mi></mrow></msub><mo>)</mo></math></span>. Based on this result, we construct a class of regular spectra of <span><math><msub><mrow><mi>μ</mi></mrow><mrow><mi>A</mi><mo>,</mo><mi>D</mi></mrow></msub></math></span>. Furthermore, we analyze the Beurling dimensions of the spectra and obtain the optimal upper bound of Beurling dimensions of all spectra, which is in stark contrast with the case of self-similar spectral measures. As an application of our results, we obtain an intermediate property about the Beurling dimension of the spectra.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"548 1","pages":"Article 129385"},"PeriodicalIF":1.2,"publicationDate":"2025-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143445256","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 : 2025-02-18DOI: 10.1016/j.jmaa.2025.129388
Nikita Evseev
We study continuous mappings on the Heisenberg group that preserve horizontal Brownian motion up to a time change. It is proved that only harmonic morphisms possess this property.
我们研究了海森堡群上保持水平布朗运动直至时间变化的连续映射。研究证明，只有谐波态射才具有这一性质。
{"title":"Brownian path preserving mappings on the Heisenberg group","authors":"Nikita Evseev","doi":"10.1016/j.jmaa.2025.129388","DOIUrl":"10.1016/j.jmaa.2025.129388","url":null,"abstract":"<div><div>We study continuous mappings on the Heisenberg group that preserve horizontal Brownian motion up to a time change. It is proved that only harmonic morphisms possess this property.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"548 2","pages":"Article 129388"},"PeriodicalIF":1.2,"publicationDate":"2025-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143454612","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-02-18DOI: 10.1016/j.jmaa.2025.129384
Jia-Long Chen
<div><div>Let <span><math><msubsup><mrow><mo>{</mo><mo>(</mo><msub><mrow><mi>A</mi></mrow><mrow><mi>k</mi></mrow></msub><mo>,</mo><msub><mrow><mi>D</mi></mrow><mrow><mi>k</mi></mrow></msub><mo>)</mo><mo>}</mo></mrow><mrow><mi>k</mi><mo>=</mo><mn>1</mn></mrow><mrow><mo>∞</mo></mrow></msubsup></math></span> be a sequence of pairs, where <span><math><msub><mrow><mi>D</mi></mrow><mrow><mi>k</mi></mrow></msub></math></span> is an integer vector set with <span><math><msub><mrow><mi>sup</mi></mrow><mrow><mi>d</mi><mo>∈</mo><msub><mrow><mi>D</mi></mrow><mrow><mi>k</mi></mrow></msub></mrow></msub><mo></mo><mo>∥</mo><mi>d</mi><mo>∥</mo><mo><</mo><mo>∞</mo></math></span> and <span><math><msub><mrow><mi>A</mi></mrow><mrow><mi>k</mi></mrow></msub></math></span> is an integer expansive matrix. Associated with the sequence <span><math><msubsup><mrow><mo>{</mo><mo>(</mo><msub><mrow><mi>A</mi></mrow><mrow><mi>k</mi></mrow></msub><mo>,</mo><msub><mrow><mi>D</mi></mrow><mrow><mi>k</mi></mrow></msub><mo>)</mo><mo>}</mo></mrow><mrow><mi>k</mi><mo>=</mo><mn>1</mn></mrow><mrow><mo>∞</mo></mrow></msubsup></math></span>, Moran measure <span><math><msub><mrow><mi>μ</mi></mrow><mrow><mo>{</mo><msub><mrow><mi>A</mi></mrow><mrow><mi>k</mi></mrow></msub><mo>}</mo><mo>,</mo><mo>{</mo><msub><mrow><mi>D</mi></mrow><mrow><mi>k</mi></mrow></msub><mo>}</mo></mrow></msub></math></span> is defined by<span><span><span><math><msub><mrow><mi>μ</mi></mrow><mrow><mo>{</mo><msub><mrow><mi>A</mi></mrow><mrow><mi>k</mi></mrow></msub><mo>}</mo><mo>,</mo><mo>{</mo><msub><mrow><mi>D</mi></mrow><mrow><mi>k</mi></mrow></msub><mo>}</mo></mrow></msub><mo>=</mo><msub><mrow><mi>δ</mi></mrow><mrow><msubsup><mrow><mi>A</mi></mrow><mrow><mn>1</mn></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msubsup><msub><mrow><mi>D</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow></msub><mo>⁎</mo><msub><mrow><mi>δ</mi></mrow><mrow><msubsup><mrow><mi>A</mi></mrow><mrow><mn>1</mn></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msubsup><msubsup><mrow><mi>A</mi></mrow><mrow><mn>2</mn></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msubsup><msub><mrow><mi>D</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></msub><mo>⁎</mo><mo>⋯</mo><mo>.</mo></math></span></span></span> Assume that <span><math><mo>{</mo><mi>x</mi><mo>∈</mo><msup><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo></mrow><mrow><mi>n</mi></mrow></msup><mo>:</mo><msub><mrow><mo>∑</mo></mrow><mrow><mi>d</mi><mo>∈</mo><msub><mrow><mi>D</mi></mrow><mrow><mi>k</mi></mrow></msub></mrow></msub><msup><mrow><mi>e</mi></mrow><mrow><mn>2</mn><mi>π</mi><mi>i</mi><mo>〈</mo><mi>d</mi><mo>,</mo><mi>x</mi><mo>〉</mo></mrow></msup><mo>=</mo><mn>0</mn><mo>}</mo><mo>=</mo><msup><mrow><mi>q</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup><msup><mrow><mi>Z</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>∩</mo><msup><mrow><mo>[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo></mrow><mrow><mi>n</mi></mrow></msup><mo>﹨</mo><mo>{</mo><mn>0</mn><mo>}</mo></math></span>, we provide the necessary and
{"title":"The spectral study of a class of Moran measures in Rn","authors":"Jia-Long Chen","doi":"10.1016/j.jmaa.2025.129384","DOIUrl":"10.1016/j.jmaa.2025.129384","url":null,"abstract":"<div><div>Let <span><math><msubsup><mrow><mo>{</mo><mo>(</mo><msub><mrow><mi>A</mi></mrow><mrow><mi>k</mi></mrow></msub><mo>,</mo><msub><mrow><mi>D</mi></mrow><mrow><mi>k</mi></mrow></msub><mo>)</mo><mo>}</mo></mrow><mrow><mi>k</mi><mo>=</mo><mn>1</mn></mrow><mrow><mo>∞</mo></mrow></msubsup></math></span> be a sequence of pairs, where <span><math><msub><mrow><mi>D</mi></mrow><mrow><mi>k</mi></mrow></msub></math></span> is an integer vector set with <span><math><msub><mrow><mi>sup</mi></mrow><mrow><mi>d</mi><mo>∈</mo><msub><mrow><mi>D</mi></mrow><mrow><mi>k</mi></mrow></msub></mrow></msub><mo></mo><mo>∥</mo><mi>d</mi><mo>∥</mo><mo><</mo><mo>∞</mo></math></span> and <span><math><msub><mrow><mi>A</mi></mrow><mrow><mi>k</mi></mrow></msub></math></span> is an integer expansive matrix. Associated with the sequence <span><math><msubsup><mrow><mo>{</mo><mo>(</mo><msub><mrow><mi>A</mi></mrow><mrow><mi>k</mi></mrow></msub><mo>,</mo><msub><mrow><mi>D</mi></mrow><mrow><mi>k</mi></mrow></msub><mo>)</mo><mo>}</mo></mrow><mrow><mi>k</mi><mo>=</mo><mn>1</mn></mrow><mrow><mo>∞</mo></mrow></msubsup></math></span>, Moran measure <span><math><msub><mrow><mi>μ</mi></mrow><mrow><mo>{</mo><msub><mrow><mi>A</mi></mrow><mrow><mi>k</mi></mrow></msub><mo>}</mo><mo>,</mo><mo>{</mo><msub><mrow><mi>D</mi></mrow><mrow><mi>k</mi></mrow></msub><mo>}</mo></mrow></msub></math></span> is defined by<span><span><span><math><msub><mrow><mi>μ</mi></mrow><mrow><mo>{</mo><msub><mrow><mi>A</mi></mrow><mrow><mi>k</mi></mrow></msub><mo>}</mo><mo>,</mo><mo>{</mo><msub><mrow><mi>D</mi></mrow><mrow><mi>k</mi></mrow></msub><mo>}</mo></mrow></msub><mo>=</mo><msub><mrow><mi>δ</mi></mrow><mrow><msubsup><mrow><mi>A</mi></mrow><mrow><mn>1</mn></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msubsup><msub><mrow><mi>D</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow></msub><mo>⁎</mo><msub><mrow><mi>δ</mi></mrow><mrow><msubsup><mrow><mi>A</mi></mrow><mrow><mn>1</mn></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msubsup><msubsup><mrow><mi>A</mi></mrow><mrow><mn>2</mn></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msubsup><msub><mrow><mi>D</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></msub><mo>⁎</mo><mo>⋯</mo><mo>.</mo></math></span></span></span> Assume that <span><math><mo>{</mo><mi>x</mi><mo>∈</mo><msup><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo></mrow><mrow><mi>n</mi></mrow></msup><mo>:</mo><msub><mrow><mo>∑</mo></mrow><mrow><mi>d</mi><mo>∈</mo><msub><mrow><mi>D</mi></mrow><mrow><mi>k</mi></mrow></msub></mrow></msub><msup><mrow><mi>e</mi></mrow><mrow><mn>2</mn><mi>π</mi><mi>i</mi><mo>〈</mo><mi>d</mi><mo>,</mo><mi>x</mi><mo>〉</mo></mrow></msup><mo>=</mo><mn>0</mn><mo>}</mo><mo>=</mo><msup><mrow><mi>q</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup><msup><mrow><mi>Z</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>∩</mo><msup><mrow><mo>[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo></mrow><mrow><mi>n</mi></mrow></msup><mo>﹨</mo><mo>{</mo><mn>0</mn><mo>}</mo></math></span>, we provide the necessary and","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"548 1","pages":"Article 129384"},"PeriodicalIF":1.2,"publicationDate":"2025-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143455127","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 : 2025-02-18DOI: 10.1016/j.jmaa.2025.129391
Ming Lu, Chenxi Su
In this article, we investigate a singular limit problem for the non-isentropic magnetohydrodynamic rotation equations in an infinite slab without magnetic diffusivity. We consider the case of completely ionized gases, where both the Rossby and Mach numbers approach zero simultaneously under ill-prepared initial conditions. The limiting system resembles the two-dimensional incompressible magnetohydrodynamic equations.
{"title":"Asymptotic limit of non-isentropic compressible magnetohydrodynamic equations for rotating completely ionized gases","authors":"Ming Lu, Chenxi Su","doi":"10.1016/j.jmaa.2025.129391","DOIUrl":"10.1016/j.jmaa.2025.129391","url":null,"abstract":"<div><div>In this article, we investigate a singular limit problem for the non-isentropic magnetohydrodynamic rotation equations in an infinite slab without magnetic diffusivity. We consider the case of completely ionized gases, where both the Rossby and Mach numbers approach zero simultaneously under ill-prepared initial conditions. The limiting system resembles the two-dimensional incompressible magnetohydrodynamic equations.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"548 1","pages":"Article 129391"},"PeriodicalIF":1.2,"publicationDate":"2025-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143455129","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 : 2025-02-18DOI: 10.1016/j.jmaa.2025.129390
Nguyen Nhu Quan
In this work, we are concerned a class of anomalous diffusion equations with the nonlinearities taking values in Hilbert scales of negative order driven by fractional Brownian motion. By using the resolvent theory, fixed point argument and embeddings of fractional Sobolev spaces we prove the global solvability and give some sufficient conditions to ensure the asymptotic stability of mild solutions in the mean square moment.
{"title":"The existences and asymptotic behavior of solutions to stochastic semilinear anomalous diffusion equations","authors":"Nguyen Nhu Quan","doi":"10.1016/j.jmaa.2025.129390","DOIUrl":"10.1016/j.jmaa.2025.129390","url":null,"abstract":"<div><div>In this work, we are concerned a class of anomalous diffusion equations with the nonlinearities taking values in Hilbert scales of negative order driven by fractional Brownian motion. By using the resolvent theory, fixed point argument and embeddings of fractional Sobolev spaces we prove the global solvability and give some sufficient conditions to ensure the asymptotic stability of mild solutions in the mean square moment.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"548 1","pages":"Article 129390"},"PeriodicalIF":1.2,"publicationDate":"2025-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143445398","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 : 2025-02-18DOI: 10.1016/j.jmaa.2025.129386
Kazunori Goto , Fumihiko Hirosawa
In this paper we consider energy decay estimates for the Cauchy problems of dissipative wave equations with time dependent coefficients, in particular, the coefficients consisting of weak dissipation and very fast oscillating terms. For such a problem, which have been difficult to deal with in previous research, we prove energy decay estimates by introducing a new condition for the coefficients to evaluate oscillating cancellation of the energy, and smooth initial data such as in the Gevrey class.
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