一类非线性退化波动方程解的爆破

刘文军1王明新

数学学报 ›› 2008, Vol. 51 ›› Issue (6) : 1213-122.

数学学报 ›› 2008, Vol. 51 ›› Issue (6) : 1213-122. DOI: 10.12386/A2008sxxb0141
论文

一类非线性退化波动方程解的爆破

    刘文军1王明新
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Blow-up of Solutions for a Class of Nonlinear Degenerate Wave Equations

    Wen Jun LIUMing Xin WANG
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摘要

考虑了有界区域上一类非线性退化波动方程的初边值问题. 通过改进Vitillaro, Li和Tsai的方法, 建立了非正的初始能量以及正的初始能量下解的爆破结果. 同时, 还给出了解的生命跨度估计.

Abstract

We consider the initial boundary value problem for a class of nonlinear degenerate wave equations in a bounded domain. By improving the method of Vitillaro, Li and Tsai, we establish a blow up result for certain solutions with nonpositive initial energy as well as positive initial energy. Estimates of the lifespan of solutions are also given.

关键词

解的爆破 / 正的初始能量 / 退化波动方程

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刘文军1王明新. 一类非线性退化波动方程解的爆破. 数学学报, 2008, 51(6): 1213-122 https://doi.org/10.12386/A2008sxxb0141
Wen Jun LIUMing Xin WANG. Blow-up of Solutions for a Class of Nonlinear Degenerate Wave Equations. Acta Mathematica Sinica, Chinese Series, 2008, 51(6): 1213-122 https://doi.org/10.12386/A2008sxxb0141

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