×

zbMATH — the first resource for mathematics

The Stefan problem in heterogeneous media. (English) Zbl 0706.35139
The nonlinear heat-transfer equation in discontinuously heterogeneous, but piecewise homogeneous media is investigated. The existence of a weak solution in an enthalpy formulation is proved by using a Rothe method and a certain regularization of the contact conditions between the homogeneous subdomains. Phase transitions (described as a Stefan problem) and nonlinear boundary conditions are covered, too. Besides, the equation need not be of a strongly parabolic type.
Reviewer: T.Roubíček

MSC:
35R35 Free boundary problems for PDEs
35K55 Nonlinear parabolic equations
35D05 Existence of generalized solutions of PDE (MSC2000)
80A20 Heat and mass transfer, heat flow (MSC2010)
PDF BibTeX XML Cite
Full Text: DOI Numdam EuDML
References:
[1] Cannon, J. R.; DiBenedetto, E., On the existence of weak solutions to an n-dimensional Stefan problem with nonlinear boundary conditions, S.I.A.M. J. Math. Anal., Vol. 11, 632-645, (1980) · Zbl 0459.35090
[2] Friedman, A., The Stefan problem in several space variables, Trans. Amer. Math. Soc., Vol. 133, 51-87, (1968) · Zbl 0162.41903
[3] Kamenomostskaya, S., On the Stefan problem (in Russian), Mat. Sb., Vol. 53, 488-514, (1961) · Zbl 0102.09301
[4] Lions, J. L., Quelques méthodes de résolution des problèmes aux limites non linéaires, (1969), Dunod et Gauthier-Villars Paris · Zbl 0189.40603
[5] Magenes, E.; Verdi, C.; Visintin, A., Semigroup approach to the Stefan problem with nonlinear flux, Atti Acc. Lincei Rend, fis., Vol. 75, 24-33, (1983), S. VIII · Zbl 0562.35089
[6] Niezgódka, M.; Pawłow, I., A generalized Stefan problem in several space variables, Appl. Math. Optim., Vol. 9, 193-224, (1983) · Zbl 0519.35079
[7] Pawłow, I., A variational inequality approach to generalized two-phase Stefan problem in several space variables, Ann. Matem. Pura et Applicata, Vol. 131, 333-373, (1982) · Zbl 0506.35061
[8] Roubíček, T., Optimal control of a Stefan problem with state-space constraints, Numer. Math., Vol. 50, 723-744, (1987) · Zbl 0589.65056
[9] Visintin, A., Sur le problème de Stefan avec flux non linéaire, Boll. U.M.I., C-18, 63-86, (1981) · Zbl 0471.35078
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.