Energy decay for systems of semilinear wave equations with dissipative structure in two space dimensions
type: Item
instance of: scholarly article
title: Energy decay for systems of semilinear wave equations with dissipative structure in two space dimensions
zbMATH Open document ID: 1330.35256
author: Soichiro Katayama
author: Akitaka Matsumura
author: Hideaki Sunagawa
published in: NoDEA. Nonlinear Differential Equations and Applications
publication date: 2015-09-24T00:00:00Z
full work available at URL: https://arxiv.org/abs/1309.6006
review text: The Cauchy problem for a system of semilinear wave equations in two space dimensions and small initial data is studied. The nonlinear term is assumed to be the sum of a quadratic nonlinear term and a cubic nonlinear term. Inspired by known sufficient conditions for a global existence of solution -- the null conditions or the polynomial condition -- the author introduces a new structural condition for the cubic nonlinear term. It is then proved that if the quadratic null condition as well as the author's condition are satisfied, the stated Cauchy problem admits a unique global solution. Some examples of terms satisfying the author's condition are shown.
reviewed by: Claudia Simionescu-Badea
Mathematics Subject Classification ID: 35L71
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35L52
zbMATH DE Number: 6484930
zbMATH Keywords: quadratic nonlinear term
zbMATH Keywords: cubic nonlinear term
zbMATH Keywords: null conditions
zbMATH Keywords: polynomial condition
MaRDI profile type: Publication
OpenAlex ID: W2089514516
arXiv ID: 1309.6006
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DOI: 10.1007/S00030-014-0297-7
description: scientific article