Classification of Initial Energy in a Pseudo-parabolic Equation with Variable Exponents and Singular Potential

被引：2

作者：

Sun, Xizheng ^{[1
]}

Han, Zhiqing ^{[1
]}

Liu, Bingchen ^{[2
]}

机构：

[1] Dalian Univ Technol, Sch Math Sci, Dalian 116024, Peoples R China

[2] China Univ Petr, Coll Sci, Qingdao 266580, Peoples R China

来源：

BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY | 2024年 / 50卷 / 01期

关键词：

Pseudo-parabolic equation; Singular potential; Variable exponent; Variational method; Mountain pass level; TIME BLOW-UP; GLOBAL WELL-POSEDNESS; FILTRATION EQUATION; EXISTENCE;

D O I：

10.1007/s41980-023-00844-x

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This paper deals with a pseudo-parabolic equation with singular potential and variable exponents. First, we determine the existence and uniqueness of weak solutions in Sobolev spaces with variable exponents. Second, in the frame of variational methods, we classify the blow-up and the global existence of solutions completely using the initial energy. Third, we obtain lower and upper bounds of blow-up time for all possible initial energy. The results in this paper are compatible with the corresponding problems with constant exponents. Part results of the paper extend the recent ones in Lian et al. (J Differ Equ 269:4914-4959, 2020), Xu and Su (J Funct Anal 264:2732-2763, 2013), and Liu and Yu (J Funct Anal 274:1276-1283, 2018).

引用

页数：39

共 50 条

[1] Classification of Initial Energy in a Pseudo-parabolic Equation with Variable Exponents and Singular Potential
Xizheng Sun
Zhiqing Han
Bingchen Liu
[J]. Bulletin of the Iranian Mathematical Society, 2024, 50
[2] Classification of initial energy in a pseudo-parabolic equation with variable exponents
Li, Fengjie
Liu, Jiaqi
Liu, Bingchen
[J]. ANALYSIS AND MATHEMATICAL PHYSICS, 2021, 11 (04)
[3] Classification of initial energy in a pseudo-parabolic equation with variable exponents
Fengjie Li
Jiaqi Liu
Bingchen Liu
[J]. Analysis and Mathematical Physics, 2021, 11
[4] Note on a higher order pseudo-parabolic equation with variable exponents
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[J]. MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2023, 46 (16) : 16840 - 16856
[5] Blow up in a semilinear pseudo-parabolic equation with variable exponents
Messaoudi S.A.
Talahmeh A.A.
[J]. ANNALI DELL'UNIVERSITA' DI FERRARA, 2019, 65 (2) : 311 - 326
[6] Classification of Initial Energy to a Pseudo-parabolic Equation with p(x)-Laplacian
Sun, Xizheng
Liu, Bingchen
[J]. JOURNAL OF DYNAMICAL AND CONTROL SYSTEMS, 2023, 29 (03) : 873 - 899
[7] Classification of Initial Energy to a Pseudo-parabolic Equation with p(x)-Laplacian
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[J]. Journal of Dynamical and Control Systems, 2023, 29 : 873 - 899
[8] Blow-up phenomena for a pseudo-parabolic equation with variable exponents
Di, Huafei
Shang, Yadong
Peng, Xiaoming
[J]. APPLIED MATHEMATICS LETTERS, 2017, 64 : 67 - 73
[9] A complete classification of initial energy in a p(x)-Laplace pseudo-parabolic equation
Sun, Xizheng
Liu, Bingchen
[J]. APPLIED MATHEMATICS LETTERS, 2021, 111
[10] A complete classification of initial energy in a p(x)-Laplace pseudo-parabolic equation
Sun, Xizheng
Liu, Bingchen
[J]. Applied Mathematics Letters, 2021, 111

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