Local existence of classical solutions to first-order parabolic equations describing free boundaries

Nonlinear Analysis, Theory, Methods and Applications

Volumn 32, Issue 5, 1998, Pages 583-599

  Bailly, Jacques Herbert ^a  

^a UNIVERSITÉ PARIS SACLAY   (France)

Author keywords

Classical solutions; First order parabolic equations; Local existence

Indexed keywords

BOUNDARY CONDITIONS; DIFFERENTIAL EQUATIONS; INTERPOLATION; MATHEMATICAL MODELS; MATRIX ALGEBRA; PERTURBATION TECHNIQUES; PROBLEM SOLVING; SET THEORY; THEOREM PROVING;

FIRST-ORDER PARABOLIC EQUATIONS; FREE BOUNDARY PROBLEMS; TAYLOR FORMULA;

NONLINEAR EQUATIONS;

EID: 0032059987     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0362-546X(97)00504-X     Document Type: Article

References (18)

1. Simonett, G. and Escher, J., Maximal regularity for a free boundary problem. Preprint.
2. Duchon, J. and Robert, R., Evolution d'une interface par capillarité et diffusion de volume I. Existence locale en temps. Ann. Inst. Henri Poincaré. Analyse non-linéaire, 1984, 1, 361-378.
3. Abergel, F., Well-posedness for a Cauchy problem associated to time-dependent free boundaries with nonlocal leading terms. Com. Partial Diff. Equ. C.P.D.E., 1996, 21, 1307-1319.
4. Abergel, F. and Mossino, J., Caractérisation du problème de Muskat multidimensionnel et existence de solutions régulières. C.R. Acad. Aci. Paris, 1994, 319, Série I, 35-40.
5. Chen, X., Hong, J. and Yi, F., Existence, uniqueness and regularity of classical solutions of the Mullins-Sekerka problem. Preprint.
6. Chen, X., The Hele-Shaw problem and area preserving curve-shorting motions. Arch. Rat. Mech. Anal., 1993, 123, 117-151.
7. Yi, F., Tao, Y. and Lin, Z. The quasi-stationary Stefan problem as a limit of the Mullins-Sekerka problem. Preprint.
8. DaPrato, G. and Grivard, P., Equations d'évolution abstraites non-linéaires de type parabolique. Ana. Mat. Pura. Appl., 1979, 120, 329-396.
9. DaPrato, G. and Grivard, P., Sommes d'opérateurs linéaires et équations différentielles opérationnelles. J. Math. Pures. Appl., 1975, 54, 305-387.
10. Angenent, S. B., Nonlinear analytic semiflows. Proc. Roy. Soc. Edinburgh, 1990, 115A, 91-107.
11. Amann, H., Linear and Quasilinear Parabolic Problems. Birkhaüser, 1995.
12. Lunardi, A., Analytic Semigroups and Optimal Regularity in Parabolic Equations. Birkhaüser, Basel, 1994.
13. Scheid, J. F., Etude théorique et numérique de l'évolution morphologique d'interfaces. Thèse de Doctorat, 1994.
14. Doubrovine, B., Novikov, S. and Fomenko, A., Géométrie contemporaine, méthodes et applications, Vol. 1. Mir Edition, Moscou, 1982.
15. Alinhac, S. and Gérard, P., Operateurs pseudo-différentiels et théorème de Nash-Moser. Publications universitaires scientifiques, Université Paris-Sud, 1989.
16. Hörmander, L., The Analysis of Linear Partial Differential Operators, Vol. 3. Springer, New York, 1985.
17. Taylor, M., Pseudo-differential Operators. Princeton Univ. Press, New York, 1981.
18. Kato, T., Perturbation Theory for Linear Operators. Springer, Berlin, 1976.