Blow-up solutions for nonlinear reaction diffusion equations under Neumann boundary conditions

Abstract

In this paper, we study the blow-up solutions for the following nonlinear reaction diffusion equations with time-dependent coefficients under Neumann boundary condition

where is a bounded convex domain of with smooth boundary . By means of a first-order differential inequality technique, a lower bound on blow-up time is derived when blow-up occurs. Moreover, the conditions which imply that blow-up occurs are determined.

Keywords:

• Reaction diffusion equation
• blow-up
• lower bound

AMS Subject Classifications:

• 35K57
• 35K55
• 35K10

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [grant number 61473180], [grant number 61174082].