Blow up and exponential growth for a pseudo-parabolic equation with [formula omitted]-Laplacian and variable exponents

Abstract

Considered herein is the initial–boundary value problem for the pseudo-parabolic equation ut−Δut−div|∇u|p(x)−2∇u+ω|u|m(x)−2ut=b|u|r(x)−2u. We first give a finite time blow up criterion and then establish upper bound estimate of blow up time. In addition, we investigate the exponential growth rate of the solutions under certain conditions.