Lower Bound for the Blow-Up Time for the Nonlinear Reaction-Diffusion System in High Dimensions

الملخص EN

In this paper, we study the blow-up phenomenon for a nonlinear reaction-diffusion system with time-dependent coefficients under nonlinear boundary conditions.

Using the technique of a first-order differential inequality and the Sobolev inequalities, we can get the energy expression which satisfies the differential inequality.

The lower bound for the blow-up time could be obtained if blow-up does really occur in high dimensions.