一类非线性拟抛物方程的初边值问题

数学季刊 ›› 2010, Vol. 25 ›› Issue (3): 335-343.

一类非线性拟抛物方程的初边值问题

1. Department of Mathematics, Zhengzhou University2. Department of Mathematics and Information Science, Henan University of Urban Construction

收稿日期:2007-03-27 出版日期:2010-09-30 发布日期:2023-05-24
作者简介: GUO Hong-xia(1978- ), female, native of Linzhou, Henan, Ph.D., a lecturer of Zhengzhou University, engages in nonlinear evolution equation; HAN Xian-jun(1973- ), male, native of Yanshi, Henan, Ph.D., a lecturer of Henan University of Urban Construction, engages in nonlinear evolution equation.
基金资助:
Supported by the National Natural Science Foundation of China(10671182)；

Initial Boundary Value Problems for a Class of Non-linear Pseudo-parabolic Equation

1. Department of Mathematics, Zhengzhou University2. Department of Mathematics and Information Science, Henan University of Urban Construction

Received:2007-03-27 Online:2010-09-30 Published:2023-05-24
About author: GUO Hong-xia(1978- ), female, native of Linzhou, Henan, Ph.D., a lecturer of Zhengzhou University, engages in nonlinear evolution equation; HAN Xian-jun(1973- ), male, native of Yanshi, Henan, Ph.D., a lecturer of Henan University of Urban Construction, engages in nonlinear evolution equation.
Supported by:
Supported by the National Natural Science Foundation of China(10671182)；

摘要/Abstract

摘要： In this paper, the existence, the uniqueness, the asymptotic behavior and the non-existence of the global generalized solutions of the initial boundary value problems for the non-linear pseudo-parabolic equation u_t-αu_xx-βu_xxt=F(u)-βF (u)_xx are proved, where α, β > 0 are constants, F(s) is a given function.

关键词: non-linear pseudo-parabolic equation, initial boundary problem, global existence and uniqueness of solutions, asymptotic behavior, non-existence

Abstract: In this paper, the existence, the uniqueness, the asymptotic behavior and the non-existence of the global generalized solutions of the initial boundary value problems for the non-linear pseudo-parabolic equation u_t-αu_xx-βu_xxt=F(u)-βF (u)_xx are proved, where α, β > 0 are constants, F(s) is a given function.

Key words: non-linear pseudo-parabolic equation, initial boundary problem, global existence and uniqueness of solutions, asymptotic behavior, non-existence

中图分类号:

O175.26

郭红霞, 韩献军.

一类非线性拟抛物方程的初边值问题

[J]. 数学季刊, 2010, 25(3): 335-343.

GUO Hong-xia, HAN Xian-jun. Initial Boundary Value Problems for a Class of Non-linear Pseudo-parabolic Equation [J]. Chinese Quarterly Journal of Mathematics, 2010, 25(3): 335-343.

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