Newton’s polygon method and the local solvability of free boundary problems
- 32 Downloads
For some qualitatively new problems with free (unknown) boundary, conditions of local solvability (with respect to time) are investigated.
KeywordsCauchy Problem Free Boundary Model Problem Besov Space Free Boundary Problem
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Unable to display preview. Download preview PDF.
- 1.R. A. Adams, Sobolev Spaces, Academic Press (1975).Google Scholar
- 4.I. Brailovsky, A. Babchin, M. Frankel, and G. Sivashinsky, “Fingering instability in water-oil displacement,” to appear.Google Scholar
- 5.G. I. Barenblatt, V. M. Entov, and V. M. Ryzhik, Theory of Unsteady Filtration of Liquids and Gases [in Russian], Nedra, Moscow (1984).Google Scholar
- 8.R. Denk and L. R. Volevich, “A new class of parabolic problems connected with the Newton polygon,” to appear.Google Scholar
- 9.W. Dreyer and B. Wagner, Sharp-Interface Model for Eutectic Alloys. Pt. I. Concentration Dependent Surface Tension, Preprint N ISSN 0946-8633, Weierstrass-Institute fur Angewandte Analysis und Stochastik (2003).Google Scholar
- 12.K. K. Golovkin and V. A. Solonnikov, “On an estimate of the convolution operators,” Zap. Nauch. Sem. LOMI, 6–86 (1988).Google Scholar
- 13.S. G. Gindikin and L. R. Volevich, The Method of Newton’s Polyhedron in the Theory of Partial Differential Equations, Math. Appl. (Soviet Ser.), Vol. 86, Kluwer Academic (1992).Google Scholar
- 18.O. A. Ladyzhenskaya, Boundary Problems of Mathematical Physics [in Russian], Nauka, Moscow (1973).Google Scholar
- 19.O. A. Ladyzhenskaya and N. N. Ural’tseva, Linear and Quasilinear Equations of Elliptic Type [in Russian], Nauka, Moscow (1964).Google Scholar
- 20.S. M. Nikol’skii, Approximation of Functions of Several Variables and Imbedding Theorems, Springer (1975).Google Scholar
- 21.L. Nirenberg, Topics on Nonlinear Functional Analysis, New York Courant Inst. Math. Sciences. VIII (1974).Google Scholar
- 22.E. V. Radkevich, “The Gibbs-Thomson effect and existence conditions of a classical solution to the modified Stefan problem,” in: J. Chadam and H. Rasmussen, Free Boundary Problem Involving Solids, Pitman Research Notes in Math. Ser., Vol. 281, Longman Scientific and Technical (1992), pp. 135–142.Google Scholar
- 23.V. A. Solonnikov, “Estimates of the solution of some noncoercive initial boundary-value problems using theorems on multipliers in Fourier-Laplace integrals,” Zap. Nauch. Sem. LOMI, 220–227 (1987).Google Scholar
- 27.V. N. Vidorovich, A. E. Volpian, and G. M. Kurdiumov, Crystallization Direction and Physico-Chemical Analysis [in Russian], Khimia, Moscow (1976).Google Scholar
- 28.S. J. Watson, F. Otto, B. Y. Rubinstein, and S. H. Davis, “Coarsening dynamics for the convective Cahn-Hilliard equation,” to appear.Google Scholar
- 29.M. Zakhrchenko and E. Radkevich, “On the singular-limit problem of the extended Cahn-Hilliard model,” Tr. Sem. Petrovsk., 23, 309–336 (2004).Google Scholar
© Springer Science+Business Media, Inc. 2007