Life span bounds for reaction-diffusion equation with a space-time integral source term

In this paper, we study the blow-up phenomena of the Dirichlet initial boundary value problem for reaction-diffusion equation with a space-time integral source term. By virtue of Kaplan's technique and some new properties on the system of differential inequalities, the method of constructing blow-up sub-solutions, we establish sufficient conditions to guarantee the solution blows up in finite time and give the upper bounds of life span. Moreover, based on constructing blow-up super-solutions and combining the auxiliary function method with the modified differential inequality techniques, lower bounds of life span are derived.