Vanishing latent heat limit in a Stefan-like problem arising in biology

Nonlinear Analysis: Real World Applications

Volumn 4, Issue 2, 2003, Pages 261-285

  Hilhorst, Danielle ^a   Mimura, Masayasu ^b   Schätzle, Reiner ^c  

^a UNIVERSITÉ PARIS SACLAY   (France)

^b HIROSHIMA UNIVERSITY   (Japan)

^c UNIVERSITY OF FREIBURG   (Germany)

Author keywords

Competition diffusion systems; Spatial segregation limit analysis; Stefan like problem

Indexed keywords

EID: 0037408887     PISSN: 14681218     EISSN: None     Source Type: Journal    
DOI: 10.1016/S1468-1218(02)00009-3     Document Type: Article

References (17)

1. D.G. Aronson, J. Serrin, Local behavior of solutions of quasilinear parabolic equations, Arch. Rational Mech. Anal. 25 (1967) 81-122.
2. E.N. Dancer, D. Hilhorst, M. Mimura, L.A. Peletier, Spatial segregation limit of a competition-diffusion system, European J. Appl. Math. 10 (1999) 97-115.
3. E. DiBenedetto, A. Friedman, The ill-posed Hele-Show model and the Stefan problem for supercooled water, Trans. Amer. Math. Soc. 282 (1984) 183-204.
4. C.M. Elliott, R. Schätzle, The limit of the anisotropic double-obstacle Allen-Cahn equation, Proc. Roy. Soc. Edinburgh 126A (1996) 1217-1234.
5. L.C. Evans, A chemical diffusion-reaction free boundary problem, Nonlinear Anal. 6 (5) (1982) 455-466.
6. K. Kishimoto, H. Weinberger, The spatial homogeneity of stable equiliblia of some reaction-diffusion system on convex domain, J. Differential Equations 58 (1985) 15-21.
7. O.A. Ladyzenskaja, V.A. Solonnikov, N.N. Ural'ceva, Linear and Quasilinear Equations of Parabolic Type, American Mathematical Society, Providence, RI (Translation of Mathematical Monographs, Vol. 23, 1968).
8. H. Matano, Nonincrease of the lap-number of a solution for a one-dimensional semi-linear parabolic equation, J. Fac. Sci. Univ. Tokyo IA 29 (2) (1982) 401-441.
9. M. Mimura, Y. Yamada, S. Yotsutani, A free boundary problem in ecology, Japan J. Appl. Math. 2 (1985) 151-186.
10. M. Mimura, Y. Yamada, S. Yotsutani, Stability analysis for free boundary problems in ecology, Hiroshima Math. J. 16 (3) (1986) 477-498.
11. M. Mimura, Y. Yamada, S. Yotsutani, Free boundary problems for some reactiondiffusion equations, Hiroshima Math. J. 17 (2) (1987) 241-280.
12. p(0, T; B), Ann. Math. Pura Appl. S.4 146 (1987) 65-96.
13. D.A. Tarzia, Sur le problème de Stefan à deux phases, C. R. Acad. Sci. Paris 288 A (1979) 941-944.
14. D.A. Tarzia, Etude de l'inéquation variationelle proposée par Duvaut pour le problème de Stefan à deux phases, I, Boll. Un. Mat. Ital. 1-B (1982) 865-883.
15. D.A. Tarzia, Etude de l'inéquation variationelle proposée par Duvaut pour le problème de Stefan à deux phases, II, Boll. Un. Mat. Ital. 2-B (1983) 589-603.
16. N.S. Trudinger, Pointwise estimates and quasilinear parabolic equations, Comm. Pure Appl. Math. 21 (1968) 205-226.
17. S. Yotsutani, Stefan problems with the unilateral boundary condition on the fixed boundary II, Osaka J. Math. 20 (1983) 803-844.