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Problème mixte hyperbolique avec saut sur la condition aux limites. (A mixed hyperbolic problem with jump in the boundary condition). (French) Zbl 0652.35069
This work deals with the study of the linear mixed problem for a non- characteristic strictly hyperbolic \(N\times N\) system of degree 1, when the boundary condition has a jump along a non-characteristic hypersurface of the boundary. Assuming the uniform Lopatinski condition outside this hypersurface and a supplementary hypothesis along it, we prove a result of existence and uniqueness in the Sobolev space \(H^{\nu}\) (\(\nu\in [0,[)\). We study then propagation of conormal regularity along the jump hypersurface through the use of a tangential version of Bony’s second microlocation.
Reviewer: J.M.Delort
MSC:
35L50 Initial-boundary value problems for first-order hyperbolic systems
35R05 PDEs with low regular coefficients and/or low regular data
35D05 Existence of generalized solutions of PDE (MSC2000)
35D10 Regularity of generalized solutions of PDE (MSC2000)
35A27 Microlocal methods and methods of sheaf theory and homological algebra applied to PDEs
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