Lifespan of solutions for a fast diffusion equation

This work is concerned with the blow-up phenomenon of the Robin initial boundary value problem for a fast diffusion equation with a space-time integral source term. With the aid of the Kaplan's eigenfunction method and some new properties on the system of differential inequalities, we establish sufficient conditions to ensure the solution blows up in finite time and obtain the upper bounds of lifespan. Meantime, by constructing blow-up super-solutions and combining the auxiliary function method with the modified differential inequality techniques, lower bounds of lifespan are derived.