Existence of a solution of the wave equation with nonlinear damping and source terms

Vladimir Georgiev; Grozdena Todorova

doi:10.1006/jdeq.1994.1051

Existence of a solution of the wave equation with nonlinear damping and source terms

Vladimir Georgiev, Grozdena Todorova

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437 Citations (Scopus)

Abstract

We study the nonlinear wave equation involving the nonlinear damping term u_t |u_t|^m-1 and a source term of type u |u|^p-1. For 1 < p ≤ m we prove a global existence theorem with large initial data. For 1 < m < p a blow-up result is established for sufficiently large initial data.

Original language	English
Pages (from-to)	295-308
Number of pages	14
Journal	Journal of Differential Equations
Volume	109
Issue number	2
DOIs	https://doi.org/10.1006/jdeq.1994.1051
Publication status	Published - 1994 Apr 15
Externally published	Yes

ASJC Scopus subject areas

Analysis
Applied Mathematics

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title = "Existence of a solution of the wave equation with nonlinear damping and source terms",

abstract = "We study the nonlinear wave equation involving the nonlinear damping term ut |ut|m-1 and a source term of type u |u|p-1. For 1 < p ≤ m we prove a global existence theorem with large initial data. For 1 < m < p a blow-up result is established for sufficiently large initial data.",

author = "Vladimir Georgiev and Grozdena Todorova",

year = "1994",

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AU - Todorova, Grozdena

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AB - We study the nonlinear wave equation involving the nonlinear damping term ut |ut|m-1 and a source term of type u |u|p-1. For 1 < p ≤ m we prove a global existence theorem with large initial data. For 1 < m < p a blow-up result is established for sufficiently large initial data.

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Existence of a solution of the wave equation with nonlinear damping and source terms

Abstract

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