Blow-up analysis for a reaction-diffusion equation with gradient absorption terms

Abstract

This paper deals with the blow-up phenomena of solution to a reaction-diffusion equation with gradient absorption terms under nonlinear boundary flux. Based on the technique of modified differential inequality and comparison principle, we establish some conditions on nonlinearities to guarantee the solution exists globally or blows up at finite time. Moreover, some bounds for blow-up time are derived under appropriate measure in higher dimensional spaces (N≥2).

Keywords

• reaction-diffusion equation
• gradient absorption term
• nonlinear boundary flux
• bounds for blow-up time