Differential and Integral Equations

Asymptotic behaviour of solutions of parabolic reaction-diffusion systems

Joanna Rencławowicz

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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

Permanent link to this document
https://projecteuclid.org/euclid.die/1356060872

Mathematical Reviews number (MathSciNet)
MR1870469

Zentralblatt MATH identifier
1011.35021

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

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


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