Global existence for systems of nonlinear wave and klein-gordon equations with compactly supported initial data

Soichiro Katayama

doi:10.3934/cpaa.2018071

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2018, Volume 17, Issue 4: 1479-1497. Doi: 10.3934/cpaa.2018071

This issue Previous Article Local and global existence of solutions to a strongly damped wave equation of the $ p $-Laplacian type Next Article Blow up for initial boundary value problem of critical semilinear wave equation in two space dimensions

Global existence for systems of nonlinear wave and klein-gordon equations with compactly supported initial data

Soichiro Katayama

Department of Mathematics, Graduate School of Science, Osaka University, Toyonaka, Osaka 560-0043, JAPAN

Received: June 2017

Revised: November 2017

Published: April 2018

The author is supported by JSPS, Grant-in-Aid for Scientific Research (C) (JSPS KAKENHI Grant Number JP26400168).

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Abstract

We consider the Cauchy problem for coupled systems of nonlinear wave and Klein-Gordon equations in three space dimensions. The author previously proved the small data global existence for rapidly decreasing data under a certain condition on nonlinearity. In this paper, we show that we can weaken the condition, provided that the initial data are compactly supported.

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Mathematics Subject Classification: Primary: 35L70; Secondary: 35L52.

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References

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