On a Porous Medium Equation with Weighted Inner Source Terms and a Nonlinear Nonlocal Boundary Condition

This paper deals with the asymptotic behavior for a porous medium equation with weighted inner source terms and a nonlinear nonlocal boundary condition. We find the influences of spacetime-varying weight functions and competitive relationship between the multiple nonlinearities on whether determining blow-up of solutions or not, and establish the blow-up rate estimate under some appropriate conditions. Especially, our results include the situation of slow, linear and fast diffusion.