GLOBAL EXISTENCE TO THE INITIAL-BOUNDARY VALUE PROBLEM FOR A SYSTEM OF NONLINEAR DIFFUSION AND WAVE EQUATIONS II

被引：1

作者：

Nakao, Mitsuhiro ^{[1
]}

机构：

[1] Kyushu Univ, Fac Math, Moto Oka 744, Fukuoka, Fukuoka 8190395, Japan

来源：

KYUSHU JOURNAL OF MATHEMATICS | 2018年 / 72卷 / 02期

关键词：

global existence; system; nonlinear diffusion equation; nonlinear wave equation; LINEAR PARABOLIC EQUATIONS; BEHAVIOR;

D O I：

10.2206/kyushujm.72.287

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove the global existence and uniqueness of the strong solution pair (u, v) to the initial-boundary value problem for coupled equations of an m-Laplacian-type diffusion equation and a nonlinear wave equation. The interaction of the two equations is given through nonlinear source terms f (u, v) and g(u, v). To derive the required a priori estimates we employ a 'loan' method. The estimation of the L-infinity-norm of solutions of the nonlinear parabolic equation due to Moser's iteration method is a key step of our argument.

引用

页码：287 / 306

页数：20

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