Asymptotic behaviour of solutions of parabolic reaction-diffusion systems

Abstract

This paper studies the asymptotic behaviour near blow-up points of solutions of the system $$ u_t = \Delta u + u^{p_1} v^{q_1} $$ $$v_t = \Delta v + u^{p_2} v^{q_2} $$ with nonnegative, bounded initial data. We derive estimates on the blow-up rates, then we prove a Liouville-type theorem and finally, making use of these results, we obtain the description of possible blow-up patterns.