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

Vladimir Simeonov Gueorguiev, Grozdena Todorova

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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.

Original languageEnglish
Pages (from-to)295-308
Number of pages14
JournalJournal of Differential Equations
Volume109
Issue number2
DOIs
Publication statusPublished - 1994 Apr 15
Externally publishedYes

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ASJC Scopus subject areas

  • Analysis

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