Couches limites pour des problèmes mixtes hyperboliques

 Access to full text

 Full (PDF)

1. [Ba]— C Bardos, Problèmes aux limites pour les équations du premier ordre, Ann. Sci. Ecol. Norm. Sup.3, (1970), 185-233. Zbl0202.36903MR274925
2. [BBB]— C. Bardos, D. Brézis, H. Brézis, Perturbations singulières et prolongements maximaux d'opérateurs positifs, Arch. Rational Mech. Anal.53, (1973), 69-100. Zbl0281.47028MR348247
3. [BR]— C. Bardos, J. Rauch, Maximal positive boundary value problems as limits of singular perturbation problems, Trans. Amer. Math. Soc., 270, (1982), 377-408. Zbl0485.35010MR645322
4. [Bé] — M. Bézard, Problème aux limites pour le système de Vlasov-Maxwell, exposé N.4, séminaire Equations aux Dérivées Partielles de l'Ecole Polytechnique, 1992-93, et preprint n.1029, Ecole Polytechnique, 1992. MR1240545
5. [F]— K.O. Friedrichs, Symmetric positive systems of differential equations, Comm. Pure Appl. Math.7, (1954), 345-392. Zbl0059.08902MR62932
6. [G1] — O Guès, Article en préparation. 
7. [G2]— O Guès, Prolème mixte hyperbolique quasilinéaire caractéristique, Comm. Part. Diff. Equa., 15 (5), (1990), 595-645. Zbl0712.35061MR1070840
8. [I] — A.M. Il'in, Matching of asymptotic expansions of solutions of boundary value problems, Translations of Mathematical Monographs, vol 102, Amer. Math. Soc., Providence, R. I., 1992. Zbl0754.34002MR1182791
9. [JR]— J.-L. Joly, J. Rauch, Justification of multidimensional single phase semilinear geometric optics, Trans. Amer. Math. Soc.330, (1992), 599-624. Zbl0771.35010MR1073774
10. [Ka]— T. Kato, Nonstationary flows of viscous and ideal fluids in R3, J. Funct. Anal., 9, (1972),296-305. Zbl0229.76018MR481652
11. [KL]— H-O. Kreiss, J. Lorenz, Initial boundary value problems and the Navier-Stokes equations, Pure and Applied Mathematics, vol. 136, Academic Press, London, 1989. Zbl0689.35001MR998379
12. [KM]— S Klainerman, A. Majda, Singular limits of quasilinear hyperbolic systems with large parameters and the incompressible limit of compressible fluids, Comm. Pure Appl. Math., 34 (1981), 481-524. Zbl0476.76068MR615627
13. [Lev]— N Levinson, The first boundary value problem for εΔu + A(x, y)ux + B(x,y)uy + C(x, y)u = D(x, y) for small ε, Ann. Math.5, (1950), 428-445. Zbl0036.06801
14. [L] — J-L. Lions, Perturbations singulières dans les problèmes aux limites et en contrôle optimal, Lecture Notes in Math., N. 323, Springer-Verlag, 1973. Zbl0268.49001MR600331
15. [LP]— P Lax, R. Philips, Local boundary conditions for dissipative symmetric linear differential operators, Comm. Pure Appl. Math., 13, (1960), 427-455. Zbl0094.07502MR118949
16. [LSU]— O.A. Ladyzhenskaya, V.A. Solonnikov, N.N. Ural'ceva, Linear and quasilinear equations of parabolic type, Moscou1967, et Trans. Math. Monographs, vol. 23, Amer. Math. Soc., Providence, RI, 1968. Zbl0174.15403MR241822
17. [O]— O. Oleinik, Linear equations of second order, Mat. Sb.69, (1966), 111-140, et Amer. Math. Soc. Transl. Sries 2, 65, (1967), 167-200. MR193383
18. [R]— J Rauch, Symmetric positive systems with boundary characteristic of constant multiplicity, Trans. Amer. Math. Soc.291, (1985), 167-185. Zbl0549.35099MR797053
19. [RR]— J. Rauch, M. Reed, Bounded, stratified, and striated solutions of hyperbolic systems, Nonlinear Partial Differential Equations and their Applications, vol.9, Pitman Res. Notes in Math., 181, Longman Scientific and Technical, Harlow, (1988), 334-351. Zbl0695.35124MR992654
20. [VL1]— M.I. Vishik, L.A. Lyusternik, Asymptotic behavior of solutions of linear differential equations with large or quickly changing coefficients and boundary condition, Russian Math. Surveys4, (1960), 23-92. Zbl0098.06501
21. [VL2] — M.I. Vishik, L.A. Lyusternik, Regular degeneration and boundary layers for linear differential equations with small parameter, Uspek. Math. Nauk.12 (1957), 3-122, Amer. Math. Soc. Transl. (2) 20 (1962), 239-264. Zbl0122.32402MR136861

1. Olivier Guès, Perturbations visqueuses de problèmes mixtes hyperboliques et couches limites