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Criterion of singularity formation for radial solutions of the pressureless Euler-Poisson equations in exceptional dimension
IF 1.2 3区 数学 Q1 MATHEMATICS Pub Date : 2025-02-20 DOI: 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 C1-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.
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引用次数: 0
The weighted Bergman spaces and complex reflection groups
IF 1.2 3区 数学 Q1 MATHEMATICS Pub Date : 2025-02-18 DOI: 10.1016/j.jmaa.2025.129366
Gargi Ghosh
We consider a bounded domain ΩCd 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 Ω/G. Consequently, formulae involving the weighted Bergman kernels and projections of Ω and Ω/G 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 Ω/G) have been deduced to demonstrate the merit of the described formulae.
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引用次数: 0
Pointwise convergence for the heat equation on tori Tn and waveguide manifold Tn×Rm
IF 1.2 3区 数学 Q1 MATHEMATICS Pub Date : 2025-02-18 DOI: 10.1016/j.jmaa.2025.129389
Divyang G. Bhimani, Rupak K. Dalai
We completely characterize the weighted Lebesgue spaces on the torus Tn and waveguide manifold Tn×Rm 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.
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引用次数: 0
Asymptotic results for dynamic contagion processes with different exciting functions and application to risk models
IF 1.2 3区 数学 Q1 MATHEMATICS Pub Date : 2025-02-18 DOI: 10.1016/j.jmaa.2025.129392
Shamiksha Pandey , Dharmaraja Selvamuthu , Paola Tardelli
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.
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引用次数: 0
Spectra of the Sierpiński type spectral measure and their Beurling dimensions
IF 1.2 3区 数学 Q1 MATHEMATICS Pub Date : 2025-02-18 DOI: 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 μA,D. We first give a sufficient and necessary condition for the family of exponential functions {e2πiλ,x:λΛ} to be a maximal orthogonal set in L2(μA,D). Based on this result, we construct a class of regular spectra of μA,D. 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.
西尔皮斯基类型度量是几何度量理论、动力系统和概率专家研究的一类重要的自参量。本文研究了 Sierpiński 型谱度量 μA,D 的谱结构。我们首先给出了指数函数族 {e-2πi〈λ,x〉:λ∈Λ}是 L2(μA,D) 中最大正交集的充分必要条件。基于这一结果,我们构建了一类 μA,D 的正则谱。此外,我们还分析了谱的贝林维度,并得到了所有谱的贝林维度的最优上界,这与自相似谱度量的情况形成了鲜明对比。作为我们结果的应用,我们得到了关于谱的贝林维度的中间属性。
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引用次数: 0
Brownian path preserving mappings on the Heisenberg group
IF 1.2 3区 数学 Q1 MATHEMATICS Pub Date : 2025-02-18 DOI: 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。
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引用次数: 0
The spectral study of a class of Moran measures in Rn
IF 1.2 3区 数学 Q1 MATHEMATICS Pub Date : 2025-02-18 DOI: 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":"&lt;div&gt;&lt;div&gt;Let &lt;span&gt;&lt;math&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mo&gt;{&lt;/mo&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;}&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;∞&lt;/mo&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;/math&gt;&lt;/span&gt; be a sequence of pairs, where &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; is an integer vector set with &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;sup&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;⁡&lt;/mo&gt;&lt;mo&gt;∥&lt;/mo&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;mo&gt;∥&lt;/mo&gt;&lt;mo&gt;&lt;&lt;/mo&gt;&lt;mo&gt;∞&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; and &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; is an integer expansive matrix. Associated with the sequence &lt;span&gt;&lt;math&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mo&gt;{&lt;/mo&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;}&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;∞&lt;/mo&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;/math&gt;&lt;/span&gt;, Moran measure &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;μ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;{&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;}&lt;/mo&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mo&gt;{&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;}&lt;/mo&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; is defined by&lt;span&gt;&lt;span&gt;&lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;μ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;{&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;}&lt;/mo&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mo&gt;{&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;}&lt;/mo&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;δ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;⁎&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;δ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;⁎&lt;/mo&gt;&lt;mo&gt;⋯&lt;/mo&gt;&lt;mo&gt;.&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt; Assume that &lt;span&gt;&lt;math&gt;&lt;mo&gt;{&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;:&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mo&gt;∑&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;e&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mi&gt;π&lt;/mi&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;mo&gt;〈&lt;/mo&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;〉&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;}&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;q&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;Z&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;∩&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mo&gt;[&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;﹨&lt;/mo&gt;&lt;mo&gt;{&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;}&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;, 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}
引用次数: 0
Asymptotic limit of non-isentropic compressible magnetohydrodynamic equations for rotating completely ionized gases
IF 1.2 3区 数学 Q1 MATHEMATICS Pub Date : 2025-02-18 DOI: 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.
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引用次数: 0
The existences and asymptotic behavior of solutions to stochastic semilinear anomalous diffusion equations
IF 1.2 3区 数学 Q1 MATHEMATICS Pub Date : 2025-02-18 DOI: 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.
在这项研究中,我们关注一类由分数布朗运动驱动的非线性负阶希尔伯特尺度取值的反常扩散方程。通过使用分解理论、定点论证和分数 Sobolev 空间的嵌入,我们证明了全局可解性,并给出了一些充分条件,以确保均方矩中温和解的渐近稳定性。
{"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}
引用次数: 0
On the energy decay estimate for the dissipative wave equation with very fast oscillating coefficient and smooth initial data
IF 1.2 3区 数学 Q1 MATHEMATICS Pub Date : 2025-02-18 DOI: 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.
在本文中,我们考虑了具有时间相关系数的耗散波方程的 Cauchy 问题的能量衰减估计,特别是由弱耗散和快速振荡项组成的系数。对于这种在以往研究中很难处理的问题,我们通过引入一个新的系数条件来评估能量的振荡抵消,以及平滑的初始数据(如 Gevrey 类),证明了能量衰减估计。
{"title":"On the energy decay estimate for the dissipative wave equation with very fast oscillating coefficient and smooth initial data","authors":"Kazunori Goto ,&nbsp;Fumihiko Hirosawa","doi":"10.1016/j.jmaa.2025.129386","DOIUrl":"10.1016/j.jmaa.2025.129386","url":null,"abstract":"<div><div>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.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"548 1","pages":"Article 129386"},"PeriodicalIF":1.2,"publicationDate":"2025-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143445258","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}
引用次数: 0
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Journal of Mathematical Analysis and Applications
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