Well-posedness and longtime dynamics for the finitely degenerate parabolic and pseudo-parabolic equations

IF 1.1 3区数学 Q1 MATHEMATICS

Journal of Evolution Equations Pub Date : 2024-02-26 DOI:10.1007/s00028-024-00945-y

Gongwei Liu, Shuying Tian

引用次数: 0

Abstract

We consider the initial-boundary value problem for degenerate parabolic and pseudo-parabolic equations associated with Hörmander-type operator. Under the subcritical growth restrictions on the nonlinearity f(u), which are determined by the generalized Métivier index, we establish the global existence of solutions and the corresponding attractors. Finally, we show the upper semicontinuity of the attractors in the topology of \(H_{X,0}^1(\Omega )\).

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有限退化抛物和伪抛物方程的好求和长时间动力学

我们考虑了与赫曼德型算子相关的退化抛物和伪抛物方程的初始边界值问题。在由广义梅蒂维尔指数决定的非线性 f(u) 的次临界增长限制下，我们确定了解的全局存在性和相应的吸引子。最后，我们证明了吸引子在\(H_{X,0}^1(\Omega )\)拓扑中的上半连续性。

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