Journal of the Mathematical Society of Japan

On global smooth solutions to the initial-boundary value problem for quasilinear wave equations in exterior domains

Mitsuhiro NAKAO

Full-text: Open access

Abstract

We consider the initial-boundary value problem for the standard quasilinear wave equation:

utt-div{σ(|u|2)u}+a(x)ut=0 in Ω×[0,)

u(x,0)=u0(x) and ut(x,0)=u1(x) and u|Ω=0

where Ω is an exterior domain in RN, σ(v) is a function like σ(v)=1/1+v and a(x) is a nonnegative function. Under two types of hypotheses on a(x) we prove existence theorems of global small amplitude solutions. We note that a(x)ut is required to be effective only in localized area and no geometrical condition is imposed on the boundary Ω.

Article information

Source
J. Math. Soc. Japan, Volume 55, Number 3 (2003), 765-795.

Dates
First available in Project Euclid: 3 October 2007

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1191419002

Digital Object Identifier
doi:10.2969/jmsj/1191419002

Mathematical Reviews number (MathSciNet)
MR1978222

Zentralblatt MATH identifier
1030.35124

Subjects
Primary: 35B35: Stability 35L70: Nonlinear second-order hyperbolic equations

Keywords
Decay Global solution Localized dissipation Quasilinear wave equation Exterior domain

Citation

NAKAO, Mitsuhiro. On global smooth solutions to the initial-boundary value problem for quasilinear wave equations in exterior domains. J. Math. Soc. Japan 55 (2003), no. 3, 765--795. doi:10.2969/jmsj/1191419002. https://projecteuclid.org/euclid.jmsj/1191419002


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