Title: Global existence and blow up of positive initial energy solution of a quasilinear wave equation with nonlinear damping and source terms

Authors: Paul A. Ogbiyele

Addresses: Department of Mathematics, University of Ibadan, Ibadan, 200284, Nigeria

Abstract: In this paper, we consider a quasilinearwave equation having nonlinear damping and source terms utt − Δut −n Σi=1 ∂/∂xi [σi(x, uxi ) + βi(x, utxi )]+ f(x, ut) = g(x, u)
and obtained global existence and blow up results under certain polynomial growth conditions on the nonlinear functions σi, βi, (i = 1, 2, ..., n), f and g. We obtain global existence result for positive initial energy solution using Galerkin approximation procedure and nonexistence (blow up) result using the technique introduced by Georgiev and Todorova (1994) with little modification for our problem.

Keywords: Galerkin approximation procedure; global solution; blow up; potential well.

DOI: 10.1504/IJDSDE.2020.109105

International Journal of Dynamical Systems and Differential Equations, 2020 Vol.10 No.4, pp.299 - 320

Received: 16 Mar 2018
Accepted: 30 Nov 2018
Published online: 20 Aug 2020 *

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