## Journal of the Mathematical Society of Japan

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

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

Soichiro KATAYAMA and Hideo KUBO

#### 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