Blow-up of Solutions to Porous Medium Equations with a Nonlocal Boundary Condition and a Moving Localized Source

Abstract

This paper is devoted to the blow-up properties of solutions to the porous medium equations with a nonlocal boundary condition and a moving localized source. Conditions for the existence of global or blow-up solutions are obtained. Moreover, we prove that the unique solution has global blow-up property whenever blow-up occurs.