Differential and Integral Equations

Asymptotic behaviour of solutions of parabolic reaction-diffusion systems

Joanna Rencławowicz

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


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.

Article information

Differential Integral Equations, Volume 15, Number 2 (2002), 191-212.

First available in Project Euclid: 21 December 2012

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35K57: Reaction-diffusion equations
Secondary: 35B40: Asymptotic behavior of solutions 35K40: Second-order parabolic systems


Rencławowicz, Joanna. Asymptotic behaviour of solutions of parabolic reaction-diffusion systems. Differential Integral Equations 15 (2002), no. 2, 191--212. https://projecteuclid.org/euclid.die/1356060872

Export citation