Fujita Critical Curve for a Coupled Diffusion System with Inhomogeneous Neumann Boundary Conditions^*

* Supported by National Natural Science Foundation of China (Grants No. 11401049).

Abstract

In this paper, we establish the blow-up theorems of Fujita type for a class of exterior problems of nonlinear diffusion equations subject to inhomogeneous Neumann boundary conditions. The critical Fujita exponents are determined and it is shown that the critical curve belongs to the blow-up case under any nontrivial initial data.

Keywords:

• Fujita critical curve
• inhomogeneous term
• global existence
• blow-up
• diffusion equations

AMS Subject Classification:

• 35K65
• 35B33

Notes

* Supported by National Natural Science Foundation of China (Grants No. 11401049).