Remarks on the existence and uniqueness of global decaying solutions of the nonlinear dissipative wave equations
type: Item
instance of: scholarly article
title: Remarks on the existence and uniqueness of global decaying solutions of the nonlinear dissipative wave equations
zbMATH Open document ID: 0698.35102
DOI: 10.1007/BF02571342
author: Mitsuhiro Nakao
published in: Mathematische Zeitschrift
publication date: 1991-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/174224
review text: Global existence and uniqueness of solutions decaying at certain rate as \(t\to \infty\) are derived for small initial data to the initial boundary value problem of the nonlinear wave equation of the form: \[ u_{tt}- \Delta u+\sigma (u_ t)+f(u)=0\quad on\quad \Omega \times [0,\infty),\quad u(x,0)=u_ 0,\quad u_ t(x,0)=u_ 1\quad and\quad u|_{\partial \Omega}=0, \] where \(\Omega\) is a bounded domain in \(R^ N\) and \(\sigma\), f are functions like \(\sigma (u_ t)=| u_ t|^ ru_ t,\) \(-1<r<\infty,\) \(f(u)=| u|^{\alpha}u,\) \(\alpha >2/(N-2).\)
Mathematics Subject Classification ID: 35L70
Mathematics Subject Classification ID: 35L20
Mathematics Subject Classification ID: 35A05
zbMATH DE Number: 4144549
zbMATH Keywords: nonlinear dissipative wave equations
zbMATH Keywords: global solution
zbMATH Keywords: decay
zbMATH Keywords: global existence
zbMATH Keywords: uniqueness
zbMATH Keywords: small initial data
zbMATH Keywords: initial boundary value problem
zbMATH Keywords: nonlinear wave equation
MaRDI profile type: Publication
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OpenAlex ID: W2038013412
description: scientific article; zbMATH DE number 4144549