FINITE TIME BLOW UP OF SOLUTIONS FOR A STRONGLY DAMPED NONLINEAR KLEIN-GORDON EQUATION WITH VARIABLE EXPONENTS

This paper, we investigate a strongly damped nonlinear Klein-Gordon equation with nonlinearities of variable exponent type u(tt) - Delta u - Delta u(t) + m(2)u + vertical bar u(t)vertical bar(p(x)) (2)u(t) = vertical bar u vertical bar(q(x)) (2)u associated with initial and Dirichlet boundary conditions in a bounded domain. We obtain a nonexistence of solutions if variable exponents p (.), q (.) and initial data satisfy some conditions.