Solution to nonlinear gradient dependent systems with a balance law

Abstract

In this paper, we are concerned with the initial boundary value problem (IBVP) and with the Cauchy problem to the reaction-diffusion system $$ displaylines{ u_t-Delta u = -u^n | abla v |^p,cr v_t-d Delta v = u^n | abla v|^p, }$$ where $1leq pleq 2$, d and n are positive real numbers. Results on the existence and large-time behavior of the solutions are presented.

Keywords

• Reaction-diffusion systems
• global existence
• asymptotic behavior
• maximum principle