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

Vladimir Simeonov Gueorguiev; Grozdena Todorova

doi:10.1006/jdeq.1994.1051

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

Vladimir Simeonov Gueorguiev, Grozdena Todorova

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388 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

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ASJC Scopus subject areas

Analysis

Cite this

Gueorguiev, V. S., & Todorova, G. (1994). Existence of a solution of the wave equation with nonlinear damping and source terms. Journal of Differential Equations, 109(2), 295-308. https://doi.org/10.1006/jdeq.1994.1051

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Access to Document

10.1006/jdeq.1994.1051