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

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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. © 1994 by Academic Press, Inc.

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Georgiev, V., & 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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