Critical curves for fast diffusive polytropic filtration equations coupled through boundary

Abstract

This article deals with the critical curve of a fast diffusive polytropic filtration system coupled at the boundary condition. By constructing the self-similar supersolution and subsolution, we obtain the critical global existence curve. The critical curve of Fujita type is conjectured with the aid of some new results.

Keywords:

• critical curve
• fast diffusion
• polytropic filtration equation
• global existence
• blow-up

Mathematics Subject Classifications (2000):

• 35B33
• 35K20
• 35K57

Acknowledgements

This work was partially supported by NNSF of China (10771226), partially supported by Natural Science Foundation Project of CQ CSTC (2007BB0124), partially supported by Sichuan Center for Education Development Research(CJF0753), and partially supported by Natural Science Foundation Project of China West Normal University (07B047).