组合非线性p-拉普拉斯热方程的临界指数

IF 1.1 3区数学 Q1 MATHEMATICS

Journal of Evolution Equations Pub Date : 2023-10-26 DOI:10.1007/s00028-023-00922-x

Torebek, Berikbol T.

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引用次数: 1

摘要

研究了一类具有组合非线性的拟线性非齐次抛物型方程解的大时性。该方程是Jleli-Samet-Souplet (Proc AMS, 2020)考虑的具有组合非线性的热方程的自然扩展。首先，我们关注临界指数不连续的有趣现象。特别地，我们将填补临界情况下Jleli-Samet-Souplet结果的空白。我们还对强迫项对所考虑问题的临界行为的影响感兴趣，因此我们将根据强迫项定义另一个临界指数。

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Critical exponents for the p-Laplace heat equations with combined nonlinearities

This paper studies the large-time behavior of solutions to the quasilinear inhomogeneous parabolic equation with combined nonlinearities. This equation is a natural extension of the heat equations with combined nonlinearities considered by Jleli-Samet-Souplet (Proc AMS, 2020). Firstly, we focus on an interesting phenomenon of discontinuity of the critical exponents. In particular, we will fill the gap in the results of Jleli-Samet-Souplet for the critical case. We are also interested in the influence of the forcing term on the critical behavior of the considered problem, so we will define another critical exponent depending on the forcing term.

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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