Abstract
We present some recent results on the application of different energy methods for the study of free boundary problems. Such methods offer an alternative way when the maximum principle fails. So they are of special interest for the study of systems of equations and higher order equations. They are also useful for single equations with complicated structure making difficult the construction of super and subsolutions: this is the case, for instance, when there are unbounded data; or the nonlinearities depend on x and t; when there are first order differential terms in the equation, and so on. A monograph [1] (in preparation) collects many results in this direction. We present here several different applications.
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S.N. Antontsev, J.I. Diaz: Book in Birkhuser, 1992.
S.N. Antontsev, Dokl.Akad nauk SSSR, 216, 1974, n.3, p.p.473–476. (Translation in Soviet Math. Doklady, 15, 1974,n.3, p.p.803–807).
S.N. Antontsev, J.I. Diaz: Nonlinear Analysis, Theory, Methods Applications, 16, 4, pp.299–313.
V.N. Samokhin, Trudy Seminara imeni I.G. Petrovskogo N014, pp. 89–108 (1989) (English translation) pp.2358–2373, 1990.
J.I. Diaz, J. Hernandez: In Trends in theory and practice of Nonlinear differential equations, V. Lakshmikantham ed. Marcel Dekker, 1984, pp. 149–156.
S.I. Shmarev, Dinamika Sploshnoy Sredi. Novosibirsk 1990, V. 95,97.
S.N. Antontsev, S.I. Shmarev Dokl. Akad. Nauk SSSR, 318, 1991,n.4, p.p.777–781. (Translation in Soviet Math. Doklady, v.43, 1991).
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Antontsev, S.N., Diaz, J.I., Shmarev, S.I. (1992). New Applications of Energy Methods to Parabolic and Elliptic Free Boundary Problems. In: Antontsev, S.N., Khludnev, A.M., Hoffmann, KH. (eds) Free Boundary Problems in Continuum Mechanics. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série Internationale d’Analyse Numérique, vol 106. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8627-7_6
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DOI: https://doi.org/10.1007/978-3-0348-8627-7_6
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