The conditions for blow-up and global existence of solution for a degenerate and singular parabolic equation with a non-local source

In this work, we consider the degenerate and singular porous medium problem with a non-local source term. We prove that the such problem has a local classical solution before blow-up occur. The conditions for blow-up and non-blow-up of solutions of the problem depend on the value of constant a. In the blow-up case, we prove that the solution of the problem blows up completely. Finally, the uniform blow-up profile of the blow-up solution near the blow-up time is shown.

Reference: Nitithorn Sukwong, Wannika Sawangtong and Panumart Sawangtong