SYSTEMS OF SEMILINEAR WAVE EQUATIONS WITH MULTIPLE SPEEDS IN TWO SPACE DIMENSIONS AND A WEAKER NULL CONDITION

Minggang Cheng; Soichiro Katayama

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SYSTEMS OF SEMILINEAR WAVE EQUATIONS WITH MULTIPLE SPEEDS IN TWO SPACE DIMENSIONS AND A WEAKER NULL CONDITION

机译：SYSTEMS OF SEMILINEAR WAVE EQUATIONS WITH MULTIPLE SPEEDS IN TWO SPACE DIMENSIONS AND A WEAKER NULL CONDITION

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摘要

We consider the Cauchy problem for systems of semilinear wave equations with multiple propagation speeds in two space dimensions. The nonlinear terms are assumed to be cubic and to depend only on first derivatives of the unknowns. The null condition is one of the sufficient condition for the small data global existence for the single-speed case, and it is extended to the multiple-speed case by many authors. Recently, various weaker sufficient conditions for the small data global existence were obtained for the single-speed case. In this paper, we introduce the multiple-speed version of one of such weaker null conditions, and we show the small data global existence. The asymptotic behavior of global solutions is also investigated through associated systems of ODEs called the reduced systems.

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来源
《Communications on pure and applied analysis》 |2022年第9期|3117-3139|共23页
作者
Minggang Cheng; Soichiro Katayama;
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作者单位

Department of Mathematics, Graduate School of Science, Osaka University 1-1 Machikaneyama-cho, Toyonaka, Osaka 560-0043, Japan;

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正文语种英语
中图分类数学;
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Semilinear wave equation; null condition; weak null condition; global existence; asymptotic behavior; multiple propagation speeds;

SYSTEMS OF SEMILINEAR WAVE EQUATIONS WITH MULTIPLE SPEEDS IN TWO SPACE DIMENSIONS AND A WEAKER NULL CONDITION

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