Construction of Solutions to Heat-Type Problems with Volume Constraint via the Discrete Morse Flow

MR2351215 Karel ŠVADLENKA and Seiro OMATA Karel ŠVADLENKA and Seiro OMATA Construction of Solutions to Heat-Type Problems with Volume Constraint via the Discrete Morse Flow Funkcialaj Ekvacioj. Serio Internacia 50 2007 261--285 http://fe.math.kobe-u.ac.jp/FE/FullPapers/50-2/50_261.pdf http://www.ams.org/mathscinet-getitem?mr=MR2351215 A volume-constrained parabolic problem is investigated by means of the discrete Morse flow. We construct a weak solution as the limit of approximate weak solutions, each defined in terms of minimizers of time-discretized functionals, and the uniqueness of the weak solution is discussed. Basic properties (Hölder continuity) of the weak solution are studied and the results of applying this method to models of physical phenomena are shown. Nonlinear parabolic equation, Variational method, Discrete Morse semiflow, Volume constraint. 35K55, 47J30, 58E50. 50-261 2007 Construction of Solutions to Heat-Type Problems with Volume Constraint via the Discrete Morse Flow Karel ŠVADLENKA and Seiro OMATA Karel ŠVADLENKA and Seiro OMATA

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