Local and global wellposedness of weak solutions for the wave equation with nonlinear boundary and interior sources of supercritical exponents and damping

被引：27
|
作者：
Bociu, Lorena [1 ]
机构：
[1] Univ Nebraska, Dept Math, Lincoln, NE 68588 USA
来源：
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2009年 / 71卷 / 12期
关键词：
Wave equation; Local existence; Nonlinear damping; Boundary source; Interior source; Critical exponents; HYPERBOLIC-EQUATIONS; REGULARITY THEORY; EXISTENCE;
D O I：
10.1016/j.na.2008.11.062
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We consider the wave equation with interior and boundary nonlinear sources and damping and we are interested in local and global wellposedness of finite energy solutions. The main difficulty is represented by the fact that the Lopatinski condition fails to hold (unless the dim(Omega) = 1), and thus the analysis of the boundary nonlinearities becomes a subtle issue. (C) 2008 Elsevier Ltd. All rights reserved.
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页码：E560 / E575
页数：16
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