Local existence and global nonexistence theorems for a damped nonlinear hyperbolic equation
The initial boundary value problem for a nonlinear damped hyperbolic equation in three dimensions, with simply supported boundary is considered. Under some special conditions on the initial data and the nonlinearity function the existence of a unique local generalized solution is proved. The contraction mapping principle is used. Two results of global nonexistence of solution are shown, the one being based on the concavity method.
scientific article; zbMATH DE number 5710065