SELF-SIMILARITY AND UNIQUENESS OF SOLUTIONS FOR SEMILINEAR REACTION-DIFFUSION SYSTEMS

Author(s)

Ferreira, Lucas C. F. ^[1] ; Mateus, Eder ^[2]

Affiliation

^[1] Univ Estadual Campinas, Dept Matemat, BR-13083859 Campinas, SP - Brazil

^[2] Univ Fed Sergipe, Nucleo Matemat, BR-49500000 Itabaiana, SE - Brazil

• Document type: Journal article
• Source: Advances in Differential Equations; v. 15, n. 1-2, p. 73-98, JAN-FEB 2010.
• Web of Science Citations: 3

Abstract

We study the well posedness of the initial-value problem for a coupled semilinear reaction-diffusion system in Marcinkiewicz spaces L((p1,infinity))(Omega) x L((p2,infinity)) (Omega). The exponents p(1), p(2) of the initial-value space are chosen to allow the existence of self-similar solutions (when Omega = R(n)). As a nontrivial consequence of our coupling-term estimates, we prove the uniqueness of solutions in the scaling invariant class C({[}0, infinity); L(p1) (Omega) x L(p2) (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(p1) x L(p2) present a simple long-time behavior. (AU)

• FAPESP's process: 08/04737-0 - Equations in Singular Spaces and Optimal Mass Transportation
• Grantee: Lucas Catão de Freitas Ferreira
• Support Opportunities: Scholarships in Brazil - Post-Doctoral