Limiting behavior of strongly damped nonlinear wave equations
type: Item
instance of: scholarly article
title: Limiting behavior of strongly damped nonlinear wave equations
zbMATH Open document ID: 0561.35049
DOI: 10.1016/0022-0396(83)90098-0
author: Paul Massatt
published in: Journal of Differential Equations
publication date: 1983-01-01T00:00:00Z
review text: The author considers the equation: \(u_{tt}+\alpha Au_ t+Au=f(t,u,u_ t)\) where A is a sectorial operator on a Banach space, \(\alpha >0\) and f is a nonlinear operator periodic in t and satisfying some regularity and growth assumptions. He rewrites the equation as an abstract ordinary differential equation on a Banach space and he proves local existence, uniqueness and continuous dependence theorems. Some physical problems that are governed by an equation of this kind are also presented.
Mathematics Subject Classification ID: 35L70
Mathematics Subject Classification ID: 34G20
Mathematics Subject Classification ID: 35A05
Mathematics Subject Classification ID: 35B30
zbMATH DE Number: 3893653
zbMATH Keywords: sectorial operator
zbMATH Keywords: Banach space
zbMATH Keywords: abstract ordinary differential equation
zbMATH Keywords: local existence
zbMATH Keywords: uniqueness
zbMATH Keywords: continuous dependence
MaRDI profile type: Publication
full work available at URL: 0022-0396(83)90098-0
OpenAlex ID: W2079970514
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description: scientific article