Journal of the Mathematical Society of Japan

An alternative proof of global existence for nonlinear wave equations in an exterior domain

Soichiro KATAYAMA and Hideo KUBO

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Abstract

The aim of this article is to present a simplified proof of a global existence result for systems of nonlinear wave equations in an exterior domain. The novelty of our proof is to avoid completely the scaling operator which would make the argument complicated in the mixed problem, by using new weighted pointwise estimates of a tangential derivative to the light cone.

Article information

Source
J. Math. Soc. Japan, Volume 60, Number 4 (2008), 1135-1170.

Dates
First available in Project Euclid: 5 November 2008

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1225894036

Digital Object Identifier
doi:10.2969/jmsj/06041135

Mathematical Reviews number (MathSciNet)
MR2467873

Zentralblatt MATH identifier
1156.35058

Subjects
Primary: 35L70: Nonlinear second-order hyperbolic equations
Secondary: 35L20: Initial-boundary value problems for second-order hyperbolic equations

Keywords
nonlinear wave equation null condition exterior domain

Citation

KATAYAMA, Soichiro; KUBO, Hideo. An alternative proof of global existence for nonlinear wave equations in an exterior domain. J. Math. Soc. Japan 60 (2008), no. 4, 1135--1170. doi:10.2969/jmsj/06041135. https://projecteuclid.org/euclid.jmsj/1225894036


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