The Parabolic Equation with q(x)-Triharmonic Equation: Blow up and Growth

Abstract

In this paper, we investigate the occurrence of finite time blow-up in solutions of the homogeneous Dirichlet problem for the parabolic equation.   (1+a|u|^{p(x)-2})u_{t}+Δ_{q(x)}³u=b|u|^{r(x)-2}u.   In situations where a=0 and demonstrating exponential growth when a>0, along with negative initial energy in both cases.