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Asymptotic behaviour of nonlocal reaction–diffusion equations

✍ Scribed by M. Anguiano; P.E. Kloeden; T. Lorenz

Publisher
Elsevier Science
Year
2010
Tongue
English
Weight
385 KB
Volume
73
Category
Article
ISSN
0362-546X

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✦ Synopsis

The existence of a global attractor in L 2 (Ω) is established for a reaction-diffusion equation on a bounded domain Ω in R d with Dirichlet boundary conditions, where the reaction term contains an operator F : L 2 (Ω) → L 2 (Ω) which is nonlocal and possibly nonlinear.

Existence of weak solutions is established, but uniqueness is not required. Compactness of the multivalued flow is obtained via estimates obtained from limits of Galerkin approximations. In contrast with the usual situation, these limits apply for all and not just for almost all time instants.

📜 SIMILAR VOLUMES

Asymptotic behavior for nonlocal diffusi
Asymptotic behavior for nonlocal diffusion equations
✍ Emmanuel Chasseigne; Manuela Chaves; Julio D. Rossi 📂 Article 📅 2006 🏛 Elsevier Science 🌐 English ⚖ 220 KB

We study the asymptotic behavior for nonlocal diffusion models of the form u t = J \* uu in the whole R N or in a bounded smooth domain with Dirichlet or Neumann boundary conditions. In R N we obtain that the long time behavior of the solutions is determined by the behavior of the Fourier transform