×

zbMATH — the first resource for mathematics

Asymptotic behaviour of some nonlocal diffusion problems. (English) Zbl 1023.35016
The authors deal with a parabolic equation having a diffusion coefficient depending on a nonlocal quantity, and investigate the convergence of the solution towards a steady state. Using the dynamical systems point of view, the authors are able to treat the case of a continuum of steady states.
Reviewer: Jiaqi Mo (Wuhu)

MSC:
35B40 Asymptotic behavior of solutions to PDEs
35K55 Nonlinear parabolic equations
35K35 Initial-boundary value problems for higher-order parabolic equations
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Amann H., Linear and Quasilinear parabolic Problems 1 (1995) · Zbl 0819.35001
[2] Cazenave T., An introduction to Semilinear Evolution Equations (1998) · Zbl 0926.35049
[3] DOI: 10.1007/978-3-0348-8428-0
[4] Chipot M., Dyn. Contin. Discreate Impuls. Syst. Set. A Math. Anal. 8 pp 35– (2001)
[5] DOI: 10.1023/A:1009706118910 · Zbl 0921.35071
[6] Dautray R., Mathematical Analysis and Numerical Methods for Science and Techonologie (1992)
[7] Dieudonné J., Fondements de lapos; Analyse Moderne (1967)
[8] Gilbarg D., Elliptic partial Differential Equations of Second Order (1983) · Zbl 0562.35001
[9] Kindcrlchrer D., An Introduction in Variattonai Inequalnies and then Applications (1980)
[10] Lions J.L., Quelques Mérhodes de Résolutions des Problémes aux Limites Non Linéaires (1969)
[11] Molinet L. In preparation
[12] Raviart P.A., Introduction á l’ Analyse Numérique des Équations aux Dérivées Partielles (1983)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.