Asymptotic behaviour of solutions of parabolic reaction-diffusion systems (Q1847648)

The paper deals with the asymptotic behaviour near blow-up points of solutions to the system \[ u_t=\Delta u+u^{p_1}v^{q_1},\qquad v_t=\Delta v+u^{p_2}v^{q_2} \] with nonnegative and bounded initial data. Estimates of the blow-up rates are derived and a Liouville-type theorem is proved. Using these results, the author obtains description of possible blow-up patterns.