On the decay property of solutions to the Cauchy problem of the semilinear wave equation with a dissipative term
type: Item
instance of: scholarly article
title: On the decay property of solutions to the Cauchy problem of the semilinear wave equation with a dissipative term
zbMATH Open document ID: 0852.35099
author: Shuichi Kawashima
author: Mitsuhiro Nakao
author: Kosuke Ono
published in: Journal of the Mathematical Society of Japan
publication date: 1996-12-09T00:00:00Z
review text: For the semilinear dissipative hyperbolic Cauchy problem \[ u_{tt}- \Delta u+ f(u)= 0\text{ in } \mathbb{R}^N\times [0, \infty),\;u(t= 0)= u_0,\;u_t(t= 0)= u_1, \] where \(f\) satisfies assumptions like \(f(u)\cdot u\geq k_1 2 \int^u_0 f(s) ds\geq 0\) or \(|f(u)|\leq k_2|u|^{\alpha+ 1}\), \((k, \alpha> 0)\), detailed decay estimates of the solution are proved for the cases \(1\leq N\leq 6\), \(0< \alpha< 4/(N- 2)\). Both, energy methods and \(L^p- L^q\)-estimates for the linearized problem, are used.
Mathematics Subject Classification ID: 35L70
zbMATH DE Number: 894102
zbMATH Keywords: dissipative semilinear wave equation
zbMATH Keywords: decay estimates
reviewed by: Reinhard Racke
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2969/jmsj/04740617
OpenAlex ID: W2007694886
DOI: 10.2969/JMSJ/04740617
description: scientific article; zbMATH DE number 894102