×
Alt, Hans Wilhelm; Luckhaus, Stephan

Quasilinear elliptic-parabolic differential equations. (English) Zbl 0497.35049

Math. Z. 183, 311-341 (1983).
Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page
scan of Zbl 0497.35049

Cited in 11 Reviews
Cited in 433 Documents

MSC:

35K60 Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations
35J65 Nonlinear boundary value problems for linear elliptic equations
35D05 Existence of generalized solutions of PDE (MSC2000)
35D10 Regularity of generalized solutions of PDE (MSC2000)
35R35 Free boundary problems for PDEs
49J40 Variational inequalities

Keywords:

initial boundary value problem; elliptic parabolic differential equations; monotone continuous subgradient; growth condition; existence; regularity; uniqueness; Stefan problems
PDF BibTeX XML Cite
\textit{H. W. Alt} and \textit{S. Luckhaus}, Math. Z. 183, 311--341 (1983; Zbl 0497.35049)
Full Text: DOI EuDML
  • logo of hbz
  • logo of WorldCat

References:

[1] Alexiades, V., Cannon, J.R.: Free boundary problems in solidification of alloys. SIAM J. Math. Anal.11, 254-264 (1980) · Zbl 0436.35079
[2] Alt, H.W., DiBenedetto, E.: The flow of water and oil through porous media. Preprint · Zbl 0608.76082
[3] Alt, H.W., Luckhaus, S.: Quasilinear elliptic-parabolic differential equations. Preprint 136, SFB 123, Heidelberg (1982) · Zbl 0497.35049
[4] Alt, H.W., Luckhaus, S., Visintin, A.: Nonlinear filtration equation and the dam problem. Ann. Mat. Pura Appl. (to appear)
[5] Aronson, D.G.: Regularity properties of flows through porous media: The interface Arch. Rational Mech. Anal.37, 1-10 (1970) · Zbl 0202.37901
[6] Attouch, H., Damlamian, A.: Problèmes d’évolution dans les Hilberts et applications. J. Math. Pures Appl.54, 53-74 (1975). · Zbl 0293.35041
[7] Benilan, P.: Equations d’évolution dans un espace de Banach quelconque et applications. Thèse, Univ. Paris XI, Orsay 1972 · Zbl 0246.47068
[8] Benilan, P.: Operateursm-accretifs hémicontinues dans un espace de Banach quelconque. C.R. Acad. Sci. Paris Sér. A278, 1029-1032 (1974) · Zbl 0289.47030
[9] Benilan, P.: Existence des solutions fortes pour l’equation des milieux poreux. C.R. Acad. Sci. Paris Sér A285, 1029-1031 (1977). · Zbl 0388.35033
[10] Benilan, P., Brezis, H., Crandall, M.G.: A semilinear equation inl 1(? N ). Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4)2, 523-555 (1975) · Zbl 0314.35077
[11] Brezis, H.: Operateurs maximaux monotones et semi-groupes de contractions dans les espaces de Hilbert. Amsterdam: North-Holland 1973
[12] Cannon, J.R., DiBenedetto, E.: On the existence of weak solutions to ann-dimensional Stefan problem with nonlinear boundary conditions. SIAM J. Math. Anal.11, 632-645 (1980) · Zbl 0459.35090
[13] Crandall, M.G.: An introduction to evolution governed by accretive operators. In: Dynamical Systems. Proceedings of an International Symposium (Brown University, 1974). New York-San Francisco-London: Academic Press 1975
[14] Damlamian, A., Kenmochi, N.: Le problème de Stefan avec conditions latérales variables. Hiroshima Math. J.10, 271-293 (1980). · Zbl 0443.35080
[15] van Duyn, C.J., Peletier, L.A.: Non-stationary filtration in partially saturated porous media. Preprint Amsterdam Math. Centrum (1979) · Zbl 0502.76101
[16] Gilding, B.H.: A nonlinear degenerate parabolic equation. Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4)4, 393-432 (1977) · Zbl 0364.35027
[17] Hornung, U.: Die longitudinale Linienmethode für die ausgeartete nichtlineare Fokker-Planksche Differentialgleiching. Habilitationsschrift, Münster 1978
[18] Kröner, D., Luckhaus, S.: Flow of oil and water in a porous medium. J. Differential Equations (to appear) · Zbl 0509.35048
[19] Niezgódka, M., Pawlow, I.: A generalized Stefan problem in several space variables. Appl. Math. Optim.9, 193-224 (1983). · Zbl 0519.35079
[20] Oleinik, O.A., Kalashnikov, A.S., Yui-Lin, Chzou: The Cauchy, problem and boundary value problems for equations of the type of nonstationary filtration. Izv. Akad. Nauk SSSR Ser. Mat.22, 667-704 (1958) [Russian] · Zbl 0093.10302
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.