A porous medium equation with nonlocal boundary condition and a localized source

Abstract

This article studies the blow-up properties of solutions to a porous medium equation with nonlocal boundary condition and a general localized source. Conditions for the existence of global or blow-up solutions are obtained. Moreover, it is proved that the unique solution has global blow-up property whenever blow-up occurs. Blow-up rate estimates are also obtained for some special cases.

Keywords:

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

AMS Subject Classifications::

• 35K20
• 35K59

Acknowledgements

The authors would like to thank the referees and the editor for their valuable suggestions and comments on the original manuscript. This 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. Yuzhu Han was also supported by Graduate Innovation Fund of Jilin University.