Abstract
We study in this paper an example of «pluri-dimensional» problem i.e. a boundary value problem where the geometrical domain consists of one 3-dimensional part Ω1 and one 1-dimensional part Ω2, with a pointA common to the two boundaries (cf. Fig. 1).
The model which is studied here—and which is just an example of many other situations which can arise—consists in a parabolic (resp. hyperbolic) equation in Ω1 (resp. Ω2) with transmission conditions atA.
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Dédié au Professeur S. Faedo pour son 70éme anniversaire
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Lions, J.L. Un exemple de problème aux limites couplé parabolique-hyperbolique pour une structure pluri-dimensionnelle. Calcolo 22, 7–15 (1985). https://doi.org/10.1007/BF02576197
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DOI: https://doi.org/10.1007/BF02576197