Existence and blow-up of solutions for a porous medium equation with nonlocal boundary condition

Abstract

In this article, a porous medium equation with nonlocal boundary condition and a localized source is studied. The results of the existence of global solutions or blow-up of solutions are given. The blow-up rate estimates are also obtained under some conditions.

Keywords:

• existence
• blow-up
• porous medium equation
• nonlocal boundary condition
• localized source

AMS Subject Classifcations::

• 35K15
• 35K20
• 35K55

Acknowledgements

The project was supported by NSFC (10771085), by Key Lab of Symbolic Computation and Knowledge Engineering of Ministry of Education and by the 985 program of Jilin University.