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 ) = Δ p ( x ) z ( x , t ) + g ( z ( x , t ) ) We use a condition on the nonlinear function g ( z ) given by, ς ∫ 0 z g ( s ) d s ⩽ z g ( z ) + η z p ( x ) + μ , z > 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.