Quasilinear p(x)- Laplacian parabolic problem: upper bound for blow-up time

This paper presents a study of blow-up of solutions to a quasilinear p(x)-Laplacian problem related to the equation ${z}_{t}(x,t)={{\rm{\Delta }}}_{p(x)}z(x,t)+g(z(x,t))$ We use a condition on the nonlinear function g(z) given by, $\varsigma {\int }_{0}^{z}g(s)ds\le zg(z)+\eta {z}^{p(x)}+\mu,z\gt 0$ We extend the existing results on blow-up for a nonlinear heat equation to variable exponent case and establish an upper bound for the blow-up time with the help of concavity method.