Blow-up phenomena for a pseudo-parabolic equation with variable exponents

Abstract We consider a pseudo-parabolic equation with nonlinearities of variable exponent type u t − ν △ u t − div ( | ∇ u | m ( x ) − 2 ∇ u ) = | u | p ( x ) − 2 u , in Ω × ( 0 , T ) , associated with initial and Dirichlet boundary conditions. By means of a differential inequality technique, we obtain an upper bound for blow-up time if variable exponents p ( ⋅ ) , m ( ⋅ ) and the initial data satisfy some conditions. Also, a lower bound for blow-up time is determined under some other conditions.