On solutions of the wave equation with a sublinear dissipative term
type: Item
instance of: scholarly article
title: On solutions of the wave equation with a sublinear dissipative term
zbMATH Open document ID: 0656.35088
DOI: 10.1016/0022-0396(87)90118-5
author: Mitsuhiro Nakao
published in: Journal of Differential Equations
publication date: 1987-01-01T00:00:00Z
review text: The existence of periodic solution and a certain decay property for the nonlinear dissipative wave equation \[ u_{tt}-\Delta u+\sigma (u_ t)=f\quad in\quad R\times \Omega \quad (or\quad R^+\times \Omega) \] with the boundary condition \(u|_{\partial \Omega}=0\) are proved, where \(\Omega\) is a bounded domain in \(R^ n\) and \(\sigma\) (v) is a sublinear function, say, \(\sigma (v)=k_ 0| v|^{-r}v\), \(k_ 0>0\), \(0<r<1\).
Mathematics Subject Classification ID: 35L70
Mathematics Subject Classification ID: 35B10
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35B05
zbMATH DE Number: 4071496
zbMATH Keywords: existence
zbMATH Keywords: periodic solution
zbMATH Keywords: decay property
zbMATH Keywords: dissipative
MaRDI profile type: Publication
full work available at URL: 0022-0396(87)90118-5
OpenAlex ID: W1964503759
cites work: Q5617898
cites work: Bounded or almost periodic solution of the non linear vibrating membrane equation
cites work: Asymptotic behavior for an almost periodic, strongly dissipative wave equation
cites work: The solution by iteration of nonlinear functional equations in Banach spaces
cites work: Q3708397
cites work: Non-resonance for a strongly dissipative wave equation in higher dimensions
cites work: Some non-linear evolution equations
cites work: CONVERGENCE OF SOLUTIONS OF THE WAVE EQUATION WITH A NONLINEAR DISSIPATIVE TERM TO THE STEADY STATE
cites work: Asymptotic stability of the bounded or almost periodic solution of the wave equation with nonlinear dissipative term
cites work: Bounded, periodic or almost-periodic solutions of nonlinear hyperbolic partial differential equations
cites work: A difference inequality and its application to nonlinear evolution equations
cites work: Asymptotic stability for some nonlinear evolution equations of second order with unbounded dissipative terms
cites work: Periodic solution and decay for some nonlinear wave equations with sublinear dissipative terms
cites work: On the decay of solutions of some nonlinear dissipative wave equations in higher dimensions
cites work: Soluzioni periodiche dell'equazione delle onde con termine dissipativo non lineare
cites work: Periodic solutions of nonlinear hyperbolic partial differential equations. II
cites work: On continuity of functions with values in various Banach spaces
cites work: Q5574162
cites work: Periodic solutions of nonlinear wave-equations with a dissipative term
description: scientific article; zbMATH DE number 4071496