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January/February 2010 Self-similarity and uniqueness of solutions for semilinear reaction-diffusion systems
Lucas C.F. Ferreira, Eder Mateus
Adv. Differential Equations 15(1/2): 73-98 (January/February 2010).


We study the well posedness of the initial-value problem for a coupled semilinear reaction-diffusion system in Marcinkiewicz spaces $L^{(p_{1}, \infty)}(\Omega)\times L^{(p_{2}, \infty)}(\Omega)$. The exponents $p_{1},p_{2}$ of the initial-value space are chosen to allow the existence of self-similar solutions (when $\Omega=\mathbb{R}^{n}$). As a nontrivial consequence of our coupling-term estimates, we prove the uniqueness of solutions in the scaling invariant class $C([0,\infty);L^{p_{1}}(\Omega)\times L^{p_{2}}(\Omega))$ regardless of their size and sign. We also analyze the asymptotic stability of the solutions, show the existence of a basin of attraction for each self-similar solution and that solutions in $L^{p_{1} }\times L^{p_{2}}$ present a simple long-time behavior.


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Lucas C.F. Ferreira. Eder Mateus. "Self-similarity and uniqueness of solutions for semilinear reaction-diffusion systems." Adv. Differential Equations 15 (1/2) 73 - 98, January/February 2010.


Published: January/February 2010
First available in Project Euclid: 18 December 2012

zbMATH: 1198.35047
MathSciNet: MR2588390

Primary: 35A05, 35B, 35B40, 35K55

Rights: Copyright © 2010 Khayyam Publishing, Inc.


Vol.15 • No. 1/2 • January/February 2010
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