Blow-up analysis for a fast diffusion system with inner absorption and coupled through boundary

Abstract

This article deals with a fast diffusion system with inner absorption and coupled through boundary. As the results of the interaction among the multi-nonlinearities in the system, the critical global existence exponents were established, which are simply described via a pair of parameters solving the characteristic algebraic system introduced: the solutions are non-global for suitable large initial data if γ₁ or γ₂ > 0, and global if γ₁, γ₂ ≤ 0 for more non-trivial case of α₁ ≤ m.

Keywords:

• blow-up
• global existence
• fast diffusion
• inner absorption
• nonlinear boundary flux

AMS Subject Classifications:

• 35K50
• 35K55
• 35K65

Acknowledgements

The authors are grateful to the referee for his/her valuable suggestions on the original manuscript. This work was partially supported by NNSF of China (10771226), partially supported by Natural Science Foundation Project of CQ CSTC (2007BB0124) and partially supported by Natural Science Foundation Project of China West Normal University (07B047).