Blow-up solutions of a system of nonlinear the Klein-Gordon-Fock Type wave equations
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Nonlinear generalized Klein-Gordon type equations, blow-up, Dirichlet’s boundary conditions.Abstract
We consider the initial boundary value problem for a system of strongly damped wave equations with homogeneous Dirichlet boundary conditions and a nonlinear source term. By applying a modification of the concavity method, we demonstrate that the solutions blow up for $p<3$ with arbitrary positive initial data. Furthermore, we show that the global solvability of the problem for
$p\geq 3$.
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