Sergo Kharibegashvili and Otar Jokhadze

The Cauchy-Darboux Problem for Wave Equations with a Nonlinear Dissipative Term

abstract:
The Cauchy-Darboux problem for wave equations with a nonlinear dissipative term is investigated. The questions on the existence, uniqueness and nonexistence of a global solution of the problem are considered. The question of local solvability of the problem is also discussed.

Mathematics Subject Classification: 35L05, 35L70

Key words and phrases: Cauchy-Darboux problem, wave equation with a nonlinear dissipative term, a priori estimate, local and global solvability, nonexistence