一类具变指数和正能量的半线性双曲方程解的爆破

数学物理学报 ›› 2015, Vol. 35 ›› Issue (2): 288-293.

一类具变指数和正能量的半线性双曲方程解的爆破

王华, 贺艺军

山西大学数学科学学院太原 030006

收稿日期:2013-10-28 修回日期:2014-12-17 出版日期:2015-04-25 发布日期:2015-04-25
通讯作者: 贺艺军 E-mail:heyijun@sxu.edu.cn
作者简介:王华,E-mail:197wang@163.com
基金资助:
国家自然科学基金(61403239,11401351)和山西省自然科学基金(2014011005-2)资助

Blow-up of Solutions for a Semilinear Hyperbolic Equation with Variable Exponent and Positive Energy

Wang Hua, He Yijun

School of Mathematical Sciences, Shanxi University, Taiyuan 030006

Received:2013-10-28 Revised:2014-12-17 Online:2015-04-25 Published:2015-04-25

摘要/Abstract

摘要：

该文研究了在齐次Dirichlet边界条件下一类具变指数的半线性双曲方程 u_tt=Δ u+u^p(x). 在能量为正以及参数和初始数据满足合适的条件下, 得到了一个爆破结果.

关键词: 变指数, 爆破, 正能量

Abstract:

In this short work, we consider a class of semilinear hyperbolic equations with variable exponent u_tt=Δ u+u^p(x) with homogeneous Dirichlet boundary conditions. Under some appropriate assumptions on the parameters, and with certain initial data, a blow-up result is established with positive energy.

Key words: Variable exponent, Blow-up, Positive energy

中图分类号:

O175.2

王华, 贺艺军. 一类具变指数和正能量的半线性双曲方程解的爆破[J]. 数学物理学报, 2015, 35(2): 288-293.

Wang Hua, He Yijun. Blow-up of Solutions for a Semilinear Hyperbolic Equation with Variable Exponent and Positive Energy[J]. Acta mathematica scientia,Series A, 2015, 35(2): 288-293.

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