## Differential and Integral Equations

### Asymptotic behaviour of solutions of parabolic reaction-diffusion systems

Joanna Rencławowicz

#### 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.

#### Article information

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

Dates
First available in Project Euclid: 21 December 2012

https://projecteuclid.org/euclid.die/1356060872

Mathematical Reviews number (MathSciNet)
MR1870469

Zentralblatt MATH identifier
1011.35021

#### Citation

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