Local Hadamard well-posedness for nonlinear wave equations with supercritical sources and damping

被引：65

作者：

Bociu, Lorena ^{[2
,3
]}

Lasiecka, Irena ^{[1
]}

机构：

[1] Univ Virginia, Dept Math, Charlottesville, VA 22904 USA

[2] Univ Nebraska, Dept Math, Lincoln, NE 68588 USA

[3] CNRS INLN, Sophia Antipolis, France

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2010年 / 249卷 / 03期

基金：

美国国家科学基金会;

关键词：

Wave equation; Local existence; Nonlinear damping; Boundary source; Interior source; Critical exponents; NEUMANN BOUNDARY-CONDITIONS; HYPERBOLIC-EQUATIONS; REGULARITY THEORY; EXISTENCE;

D O I：

10.1016/j.jde.2010.03.009

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider the wave equation with supercritical interior and boundary sources and damping terms. The main result of the paper is local Hadamard well-posedness of finite energy (weak) solutions. The results obtained: (1) extend the existence results previously obtained in the literature (by allowing more singular sources): (2) show that the corresponding solutions satisfy Hadamard well-posedness conditions during the time of existence. This result provides a positive answer to an open question in the area and it allows for the construction of a strongly continuous semigroup representing the dynamics governed by the wave equation with supercritical sources and damping. (C) 2010 Elsevier Inc. All rights reserved.

引用

页码：654 / 683

页数：30

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