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2002 Asymptotic behaviour of solutions of parabolic reaction-diffusion systems
Joanna Rencławowicz
Differential Integral Equations 15(2): 191-212 (2002).

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.

Citation

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Joanna Rencławowicz. "Asymptotic behaviour of solutions of parabolic reaction-diffusion systems." Differential Integral Equations 15 (2) 191 - 212, 2002.

Information

Published: 2002
First available in Project Euclid: 21 December 2012

zbMATH: 1011.35021
MathSciNet: MR1870469

Subjects:
Primary: 35K57
Secondary: 35B40, 35K40

Rights: Copyright © 2002 Khayyam Publishing, Inc.

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Vol.15 • No. 2 • 2002
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