Problèmes de transmission sur des réseaux polygonaux pour des systèmes d'EDP

Mercier, Denis

Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 10 (2001) no. 1, pp. 107-162.

[1] Agmon (S.). - The coerciveness problem for integro-differential forms, J. d'Analyse Math., 6, 182-223,1958. | MR | Zbl

[2] Agmon (S.), Douglis (A.) and Nirenberg (L.). - Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions I, II, Com. on Pure and Applied Math., 12, 1959, 623-727; 17, 1964, 35-92. | Zbl

[3] Agranovitch (M.S.) and Vishisk (M.I.). - Elliptic problems with a parameter and parabolic problems of general type, Russian Math. Surveys, 19, 1964, 53-157. | MR | Zbl

[4] Ciarlet (P.G.). - Plates and junctions in elastic multi-structures, RMA 14, Masson, Paris, 1990. | MR | Zbl

[5] Conca (C.), Planchard (J.), Thomas (B.) et Vanninathan (M.). - Problèmes mathématiques en couplage fluide-structure. Applications aux faisceaux tubulaires, Ed. Eyrolles, Paris, 1994. | Zbl

[6] Costabel (M.), Dauge (M.) and Lafranche (Y.). - Fast semi-analytic computation of elastic edge singularities, Preprint, Univ. Rennes, 1998.

[7] Dauge (M.). - Elliptic Boundary Value Problems in Corner Domains. Smoothness And Asymptotics of Solutions, Lecture Notes in Math., Vol. 1341, Springer, Berlin 1988. | MR | Zbl

[8] Dauge (M.) and Nicaise (S.). - Oblique derivative and interface problems on polygonal domains and networks, Comm. PDE 14, 1147-1192, 1989. | MR | Zbl

[9] Kondratiev (V.A.). - Boundary value problems for elliptic equations in domains with conical or angular points,Trans. Moscow Math. Soc., 16, 1967, 227-313. | MR | Zbl

[10] Lagnese (J.E.). - Controllability of systems of interconnected membranes, Disc. Cont. Dynamical Syst., 1, 1995, 17-33. | MR | Zbl

[11] Lagnese (J.E.), Leugering (G.) and Schmidt (E.J.P.G.). - Modeling, analysis and control of dynamic elastic multi-link structures, Birkhäuser, Boston, 1994. | MR | Zbl

[12] Le Dret (H.). - Problèmes variationnels dans les multi-domaines. Modélisation des jonctions et applications, RMA 19 , Masson, Paris, 1991. | MR | Zbl

[13] Lions (J.-L.) and Magenes (E.). - Problèmes aux limites non homogènes et applications, T. 1, Dunod, 1968. | Zbl

[14] Lumer (G.). - Espaces ramifiés et diffusions sur les réseaux topologiques, C. R. Acad. Sc. Paris, Série A, 291, 1980, 627-630. | MR | Zbl

[15] Maghnouji (A.) and Nicaise (S.). - On a coupled problem between the plate equation and the membrane equation on polygons, Annales de la Faculté des sciences de Toulouse, Vol. 2, n°2, 1992. | Numdam | MR | Zbl

[16] Maz'Ya (V.G.) and Plameneskii (B.A.). - Coefficients in the asymptotics of the solutions of elliptic boundary value problems in a cone, J.of Soviet Math., 9, 1978, 750-764. | Zbl

[17] Maz'Ya (V.G.) and Plameneskii (B.A.). - Estimates in Lp and in Hölder classes and the Miranda-Agmon maximum principle for solutions of elliptic boundary value problems in domains with singular points on the boundary, Amer. Math. Soc.Trans., 123 , 1984, 1-56. | Zbl

[18] Mercier (D.) et Nicaise (S.). - Existence results for general systems of differential equations on one-dimensional networks and prewavelets approximation, Discrete and Continuous Dynamical Systems, Vol. 4, N°2, 1998, 273-300. | MR | Zbl

[19] Morand (H.J.-P.) et Ohayon (R.). - Interactions Fluides-Structures, RMA 13, Masson, Paris, 1992. | MR | Zbl

[20] Nicaise (S.). - Problèmes aux limites sur les réseaux deux-dimensionnels polygonaux topologiques, J. Math. Pures et Appl., 67, 93-113, 1998. | Zbl

[21] Nicaise (S.). - Polygonal interface problems, Series "Methoden und Verfahren der Mathematischen Physik" , 39, Peter Lang Verlag, 1993. | MR | Zbl

[22] Nicaise (S.) and Sändig (A.M.). - General Interface Problems-I, Mathematical Methods in the Applied Sciences,17 ,1994,395-429. | MR | Zbl

[23] Nicaise (S.) and Sändig (A.M.). - General Interface Problems-II, Mathematical Methods in the Applied Sciences, 17, 1994, 431-450. | MR | Zbl