Advanced Studies in Pure Mathematics

Remarks on the asymptotic behavior of global solutions to systems of semilinear wave equations

Soichiro Katayama

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Abstract

We consider the Cauchy problem for systems of semilinear wave equations with small initial data in two and three space dimensions. We first present some recent results on the global existence and the asymptotic behavior of solutions under weaker conditions than the so-called null condition. Then, restricting our attention to two-component systems with nonlinearity of the critical power, we will discuss the asymptotic behavior in more details, and show that the asymptotic behavior observed in two space dimensions can be more complicated than that in three space dimensions.

Article information

Source
Asymptotic Analysis for Nonlinear Dispersive and Wave Equations, K. Kato, T. Ogawa and T. Ozawa, eds. (Tokyo: Mathematical Society of Japan, 2019), 55-84

Dates
Received: 7 February 2015
Revised: 6 May 2017
First available in Project Euclid: 31 October 2019

Permanent link to this document
https://projecteuclid.org/ euclid.aspm/1572545240

Digital Object Identifier
doi:10.2969/aspm/08110055

Subjects
Primary: 35L71: Semilinear second-order hyperbolic equations 35B40: Asymptotic behavior of solutions

Keywords
Weak null condition Asymptotic behavior

Citation

Katayama, Soichiro. Remarks on the asymptotic behavior of global solutions to systems of semilinear wave equations. Asymptotic Analysis for Nonlinear Dispersive and Wave Equations, 55--84, Mathematical Society of Japan, Tokyo, Japan, 2019. doi:10.2969/aspm/08110055. https://projecteuclid.org/euclid.aspm/1572545240


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