S. S. Kharibegashvili, O. M. Dzhokhadze, “The Cauchy–Goursat Problem for Wave Equations with Nonlinear Dissipative Term”, Mat. Zametki, 2013, Volume 94, Issue 6,Pages <nobr>889

The Cauchy–Goursat Problem for Wave Equations with Nonlinear Dissipative Term

S. S. Kharibegashvili^a, O. M. Dzhokhadze^b

^a Tbilisi Ivane Javakhishvili State University
^b A. Razmadze Mathematical Institute, Georgian Academy of Sciences

Abstract: The Cauchy–Goursat problem for wave equations with nonlinear dissipative term is studied. The existence, uniqueness, and blow-up of global solutions of this problem are considered. The local solvability of this problem is also discussed.

Keywords: wave equation, Cauchy–Goursat problem, Volterra-type integral equation, Green's formula, dissipative term, blow-up of a solution.

UDC: 517.956.35

Received: 28.02.2011

DOI: 10.4213/mzm5617