Classification of Initial Energy to a Pseudo-parabolic Equation with p(x)-Laplacian

被引：0
作者：
Xizheng Sun
Bingchen Liu
机构：
[1] Dalian University of Technology,School of Mathematical Sciences
[2] China University of Petroleum,College of Science
来源：
Journal of Dynamical and Control Systems | 2023年 / 29卷
关键词：
(; )-Laplace pseudo-parabolic equation; Variational method; Blow-up; Energy functional; Nehari manifold; 35A01; 35B44; 35K67; 35K70; 35K92;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
This paper deals with a pseudo-parabolic equation involving p(x)-Laplacian and variable nonlinear sources. Firstly, we use the Faedo-Galerkin method to give the existence and uniqueness of weak solution in the Sobolev space with variable exponents. Secondly, in the frame of variational methods, we classify the blow-up and the global existence of solutions completely by using the initial energy, characterized with the mountain pass level, and Nehari energy. In the supercritical case, we construct suitable auxiliary functions to determine the quantitative conditions on the initial data for the existence of blow-up or global solutions. The results in this paper are compatible with the problems with constant exponents. Moreover, we give broader ranges of exponents of source and diffusion terms in the discussion of blow-up or global solutions.
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页码：873 / 899
页数：26
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