Blow-up phenomenon for a semilinear pseudo-parabolic equation involving variable source

Abstract

We consider a semilinear pseudo-parabolic equation with nonlinearities of variable exponent subject to Dirichlet boundary conditions We prove that the nonnegative classical solutions blow-up in finite time with arbitrary positive initial energy and suitable large initial values. Also, employing a differential inequality technique, we obtain an upper bound for blow-up time if and the initial value satisfies some conditions.