Asymptotically almost periodic solutions for some partial differential inclusions in $$\alpha $$ -norm

IF 1.1 3区数学 Q1 MATHEMATICS

Journal of Evolution Equations Pub Date : 2024-09-07 DOI:10.1007/s00028-024-01007-z

Mohamed Alia, Jaouad El Matloub, Khalil Ezzinbi

引用次数: 0

Abstract

In this paper, we focus on investigating the existence of mild solutions and asymptotically almost periodic mild solutions for a class of partial differential inclusions. These inclusions involve a forcing multivalued function that relies on implicit spatial derivatives of the state variable. We introduce a novel approach to simplify the complexities associated with singularities when taking the $\alpha $-norm.

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$$\alpha $$ -norm中某些偏微分夹杂的近似近周期解

在本文中，我们将重点研究一类偏微分夹杂的温和解和渐近几乎周期性温和解的存在性。这些夹杂涉及一个强制多值函数，该函数依赖于状态变量的隐式空间导数。我们引入了一种新方法来简化取 $α $-正则时与奇异性相关的复杂性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Evolution Equations 数学-数学

CiteScore

2.30

自引率

7.10%

发文量

审稿时长

>12 weeks

期刊介绍： The Journal of Evolution Equations (JEE) publishes high-quality, peer-reviewed papers on equations dealing with time dependent systems and ranging from abstract theory to concrete applications. Research articles should contain new and important results. Survey articles on recent developments are also considered as important contributions to the field. Particular topics covered by the journal are: Linear and Nonlinear Semigroups Parabolic and Hyperbolic Partial Differential Equations Reaction Diffusion Equations Deterministic and Stochastic Control Systems Transport and Population Equations Volterra Equations Delay Equations Stochastic Processes and Dirichlet Forms Maximal Regularity and Functional Calculi Asymptotics and Qualitative Theory of Linear and Nonlinear Evolution Equations Evolution Equations in Mathematical Physics Elliptic Operators