Existence and approximation of weak solutions of the Stefan problem with nonmonotone nonlinearities
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Implicit two level time discretizations are employed in transformed versions of (1), giving a (finite) sequence of nonlinear elliptic boundary value problems (for each δt) which are solved by a Galerkin method. A subsequence of the step functions constructed on D is shown to converge weakly to a weak solution of the transformed equation. If, in addition, g is monotone, the entire sequence is strongly convergent to the unique solution.
KeywordsWeak Solution Stefan Problem Unique Weak Solution Quasilinear Parabolic Equation Move Boundary Problem
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