Nonincrease of mushy region in a nonhomogeneous Stefan problem
Authors:
I. G. Götz and B. B. Zaltzman
Journal:
Quart. Appl. Math. 49 (1991), 741-746
MSC:
Primary 80A22
DOI:
https://doi.org/10.1090/qam/1134749
MathSciNet review:
MR1134749
Full-text PDF Free Access
Abstract |
References |
Similar Articles |
Additional Information
Abstract: For an arbitrary bounded solution of the Stefan problem the mushy region is nonincreasing in time in a sense of the theory of sets. This result takes place for the nonhomogeneous Stefan problem under some conditions on the behavior of a heat source in the mushy region.
- A. M. Meĭrmanov, An example of the nonexistence of a classical solution to the Stefan problem, Dokl. Akad. Nauk SSSR 258 (1981), no. 3, 547–549 (Russian). MR 620870
- M. Primicerio, Mushy regions in phase-change problems, Applied nonlinear functional analysis (Berlin, 1981) Methoden Verfahren Math. Phys., vol. 25, Peter Lang, Frankfurt am Main, 1983, pp. 251–269. MR 685609
- A. M. Meĭrmanov, Structure of the generalized solution of the Stefan problem. Periodic solutions, Dokl. Akad. Nauk SSSR 272 (1983), no. 4, 789–791 (Russian). MR 722331
- Björn Gustafsson and Jacqueline Mossino, Quelques inégalités isopérimétriques pour le problème de Stefan, C. R. Acad. Sci. Paris Sér. I Math. 305 (1987), no. 15, 669–672 (French, with English summary). MR 917593
- Joel C. W. Rogers and Alan E. Berger, Some properties of the nonlinear semigroup for the problem $u_{t}-\Delta f(u)=0$, Nonlinear Anal. 8 (1984), no. 8, 909–939. MR 753767, DOI https://doi.org/10.1016/0362-546X%2884%2990111-1
S. N. Kruzhkov, First-order multidimensional quasilinear equations, Mat. Sb. 81, no. 2, 228–255 (1970)
A. M. Meirmanov, An example of nonexistence of a classical solution of the Stefan problem, Dokl. Akad. Nauk SSSR 258, no. 3, 547–549 (1981); English transl., Soviet Math. Dokl. 23, no. 3, 564–566 (1981)
M. Primicerio, Mushy region in phase-change problem, Applied Nonlinear Functional Analysis, Lang, Frankfurt/Main, 1982, pp. 251–269
A. M. Meirmanov, The structure of a generalized solution of the Stefan problem. Periodic solutions, Dokl. Akad. Nauk SSSR 272, no. 4, 789–791 (1983); English transl., Soviet Math. Dokl. 28, no. 2, 440–443 (1983).
B. Gustafsson and J. Mossino, Quelques inégalités isopérimétriques pour le problème de Stefan, C.R. Acad. Sci. Paris Sér. I Math. 305, 669–672 (1987)
J. C. W. Rogers and A. E. Berger, Some properties of the nonlinear semigroup for the problem ${u_t} - \Delta f\left ( u \right ) = 0$, Nonlinear Anal., Theory Methods & Applications 8, 909–939 (1984)
S. N. Kruzhkov, First-order multidimensional quasilinear equations, Mat. Sb. 81, no. 2, 228–255 (1970)
Similar Articles
Retrieve articles in Quarterly of Applied Mathematics
with MSC:
80A22
Retrieve articles in all journals
with MSC:
80A22
Additional Information
Article copyright:
© Copyright 1991
American Mathematical Society
