Relative compactness in Lp of solutions of some 2m components competition-diffusion systems

Discrete and Continuous Dynamical Systems

Volumn 21, Issue 1, 2008, Pages 233-244

  Hilhorst, Danielle ^a   Iida, Masato ^b   Mimura, Masayasu ^c   Ninomiya, Hirokazu ^d  

^a UNIVERSITÉ PARIS SUD   (France)

^b IWATE UNIVERSITY   (Japan)

^c MEIJI UNIVERSITY   (Japan)

^d RYUKOKU UNIVERSITY   (Japan)

Author keywords

Frechet Kolmogoroff theorem; Reaction diffusion system; Relative compactness in L p; Singular limit

Indexed keywords

EID: 44449114800     PISSN: 10780947     EISSN: None     Source Type: Journal    
DOI: 10.3934/dcds.2008.21.233     Document Type: Conference Paper

References (7)

1. H. Brezis, "Analyse Fonctionnelle," (French) [Functional analysis] Thorie et applications, Masson, 1983.
2. S.-I. Ei, R. Ikota and M. Mimura, Segregating partition problem in competition-diffusion systems, Interfaces and Free Boundaries, 1 (1999), 57-80.
3. E. N. Dancer, D. Hilhorst, M. Mimura and L. A. Peletier, Spatial segregation limit of a competition-diffusion system, European J. Appl. Math., 10 (1999), 97-115.
4. E. C. M. Crooks, E. N. Dancer and D. Hilhorst, On long time dynamics for competition-diffusion systems with inhomogeneous boundary conditions, Topological Methods in Nonlinear Analysis, to appear.
5. E. C. M. Crooks, E. N. Dancer, D. Hilhorst, M. Mimura and H. Ninomiya, Spatial segregation limit of a competition-diffusion system with Dirichlet boundary conditions, Nonlinear Analysis: Real World Applications, 5 (2004) 645-665.
6. R. Eymard, D. Hilhorst, R. van der Hout and L. A. Peletier, A reaction-diffusion system approximation of a one-phase Stefan problem, in "Optimal Control and Partial Differential Equations," J.L. Menaldi, E. Rofman and A. Sulem eds, IOS Press Amsterdam, Berlin, Oxford, Tokyo and Washington DC (2001), 156-170.
7. D. Hilhorst, M. Iida, M. Mimura and H. Ninomiya, A competition-diffusion system approximation to the classical two-phase Stefan problem, Japan J. Ind. Appl. Math., 18 (2001), 161-180.