Global nonexistence of solutions for a system of viscoelastic wave equations with weak damping terms

Erhan Pişkin

doi:10.26637/mjm302/005

Abstract

This paper deals with the initial boundary value problem for the viscoelastic wave equations
$$
\left\{\begin{array}{c}
u_{t t}-\Delta u+\int_0^t g_1(t-\tau) \Delta u(\tau) d \tau+u_t=f_1(u, v), \\
v_{t t}-\Delta v+\int_0^t g_2(t-\tau) \Delta v(\tau) d \tau+v_t=f_2(u, v)
\end{array}\right.
$$
in a bounded domain. We obtain the global nonexistence of solutions by applying a lemma due to Y. Zhou [Global existence and nonexistence for a nonliear wave equation with damping and source terms, Math. Nacht, 278 (2005) 1341-1358].

Keywords:

Global nonexistence, viscoelastic wave equation

Mathematics Subject Classification:

35G44

Authors Imprint References Funding Related Articles Downloads

Erhan Pişkin Dicle University, Department of Mathematics, 21280 Diyarbakır, Turkey.

Pages: 168-174
Date Published: 01-04-2015
Vol. 3 No. 02 (2015): Malaya Journal of Matematik (MJM)

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