Some qualitative analysis for a parabolic equation with critical exponential nonlinearity

IF 1.1 3区数学 Q1 MATHEMATICS

Journal of Evolution Equations Pub Date : 2024-09-12 DOI:10.1007/s00028-024-01008-y

Qiang Lin, Binlin Zhang

引用次数: 0

Abstract

In this paper, we show a blowup criterion of solution for a parabolic equation with critical exponential source and arbitrary positive initial energy, which generalizes the blowup conclusions in reference (Ishiwata et al. in J Evol Equ 21:1677–1716, 2021) for subcritical and critical initial energy cases that depend on the depth of the potential well. Additionally, the continuous dependence of the local solution on the initial data is proved in detail.

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具有临界指数非线性的抛物方程的一些定性分析

本文展示了一个具有临界指数源和任意正初始能量的抛物方程解的炸毁准则，它将参考文献（Ishiwata et al. in J Evol Equ 21:1677-1716, 2021）中的炸毁结论推广到取决于势阱深度的亚临界和临界初始能量情况。此外，还详细证明了局部解对初始数据的连续依赖性。

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