The porous medium equation with a concentrated nonlinear source

Abstract

In this article, we consider the Cauchy problem for the porous medium equations with a concentrated nonlinear source. We establish the existence of generalized solutions for the problem based on some iteration technique and approximate process.

Keywords:

• porous medium equation
• concentrated nonlinear source
• existence

AMS Subject Classifications::

• 35A01
• 35K55

Acknowledgements

This work is partially supported by the National Science Foundation of China, by a Specific Foundation for Ph.D. Specialities of Educational Department of China, by the Fundamental Research Funds for the Central Universities and the Research Funds of Renmin University of China and by the Graduate Innovation fund of Jilin University (No. 20101045). The authors would like to thank to the referees for their suggestions for revisions to the manuscript.