Dynamical interface transition in ramified media with diffusion

Communications in Partial Differential Equations

Volumn 21, Issue 1-2, 1996, Pages 255-279

  Von Below, Joachim ^a   Nicaise, Serge ^a  

^a NONE

Author keywords

Dynamical interface conditions; Ramified spaces; Reaction diffusion equations; Singularities

Indexed keywords

EID: 0002986920     PISSN: 03605302     EISSN: None     Source Type: Journal    
DOI: 10.1080/03605309608821184     Document Type: Article

References (22)

1. F. ALI MEHMETI, Regular solutions of transmission and interaction problems for wave equations, Math. Meth. in the Appl. Sc., 11, 1989, 665-685.
2. F. ALI MEHMETI and S. NICAISE, Nonlinear interaction problems, Non-linear Analysis: Theory, methods and applications, 20, 1993, 27-61.
3. J. VON BELOW, Classical solvability of linear parabolic equations on networks, J. Differential Equ. 72 (1988) 316-337.
4. J. VON BELOW, A maximum principle for semilinear parabolic network equations, in: J. A. Goldstein, F. Kappel, and W. Schappacher (eds.), Differential equations with applications in biology, physics, and engineering, Lect. Not. Pure and Appl. Math. 133, M. Dekker Inc. New York, 1991, pp. 37-45.
5. J. VON BELOW, An existence result for semilinear parabolic network equations with dynamical node conditions, in: C. Bandle, J. Bemelmans, M. Chipot, M. Grüter and J. Saint Jean Paulin (eds.), Progress in partial differential equations: elliptic and parabolic problems, Pitman Research Notes in Math. Ser. 266, Longman Harlow Essex, 1992, pp. 274-283.
6. J. VON BELOW, Parabolic network equations, to appear.
7. J. VON BELOW and S. NICAISE, Dynamical interface transition in ramified media with diffusion, Report SFB 382 Universitäten Tübingen und Stuttgart, Germany, No.16, Mai 1995, = Research Report 95-3, LIMAV Université de Valenciennes et du Hainaut Cambrésis, France, 1995.
8. H. CAMERER, Die elektrotonische Spannungsausbreitung im Soma, Dendritenbaum und Axon von Nervenzellen, Dissertation, Tübingen, 1980.
9. M. DAUGE, Elliptic boundary value problems in corner domains. Smoothness and asymptotics of solutions, L.N. in Math., 1341, Springer Verlag, Berlin, 1988.
10. M. DAUGE and S. NICAISE, Oblique derivative and interface problems on polygonal domains and networks, Comm. in P.D.E., 14, 1989, 1147-1192.
11. P. GRISVARD, Elliptic problems in nonsmooth Domains, Monographs and Studies in Mathematics 21, Pitman, Boston, 1985.
12. J.-L. LIONS, Perturbations singulières dans les problèmes aux limites ei en contrôle optimal, L.N. in Math., 323, Springer Verlag, 1973.
13. J.-L. LIONS and E. MAGENES, Problèmes aux limites non-homogènes et applications, Vol. 1, Dunod, Paris, 1968.
14. G. LUMER, Connecting of local operators and evolution equation on network, L. N. in Math., 787, Springer Verlag, 1980, 219-234.
15. G. LUMER, Espaces ramifiés et diffusions sur les réseaux topologiques, C. R. Acad. Sc. Paris, Série A, 291, 1980, 627-630.
16. S. NICAISE, Polygonal interface problems, Series "Methoden und Verfahren der Mathematischen Physik", 39, Peter Lang Verlag, 1993.
17. S. NICAISE, About the Lamé system in a polygonal or polyhedral domain and a coupled problem between the Lamé system and the plate equation II: Exact controllability, Annali della Scuola Norm. Sup. Pisa, IV, 20, 1993, 163-191.
18. A. PAZY, Semigroups of linear operators and applications to Partial differential equations, Applied Math. Sc., 44, J. Springer Verlag, New-York, 1983.
19. M. H. PROTTER and H. F. WEINBERGER, Maximum principles in differential equations, Prentice-Hall, Englewood Cliffs, 1967.
20. R. E. SHOWALTER, Hilbert space methods for partial differential equations, Monographs and Studies in Mathematics, 1, Pitman, Boston, 1977.
21. M. G. SLINKO and K. HARTMANN, Methoden und Programme zur Berechnung chemischer Reaktoren, Akademie - Verlag Berlin, 1972.
22. W. WALTER, Differential and integral inequalities, J. Springer Verlag, Berlin, 1970.