Plotnikov, P. I.; Starovoĭtov, V. N. The Stefan problem with surface tension as the limit of a phase field model. (English. Russian original) Zbl 0802.35165 Differ. Equations 29, No. 3, 395-404 (1993); translation from Differ. Uravn. 29, No. 3, 461-471 (1993). The authors consider one of the versions of the phase field model where the state of a medium is described by its temperature \(\theta_ \varepsilon\) and a phase function \(\varphi_ \varepsilon\). The pair \((\theta_ \varepsilon, \varphi_ \varepsilon)\) is regarded as a solution to some initial and boundary value problem of a system of partial differential equations with a small parameter \(\varepsilon\). It is shown that this problem has a family of generalized solutions that converge to a generalized solution of the Stefan problem with surface tension as \(\varepsilon \to 0\).The solvability of the Stefan problem with surface tension has been considered in S. Luckhaus [Eur. J. Appl. Math. 1, No. 2, 101–111 (1990; Zbl 0734.35159)]. Reviewer: Shigeru Sakaguchi (Ehime) Cited in 1 ReviewCited in 10 Documents MSC: 35R35 Free boundary problems for PDEs 35D99 Generalized solutions to partial differential equations 35B25 Singular perturbations in context of PDEs 35B30 Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs Keywords:phase field model; Stefan capillary problem; interface mean curvature Citations:Zbl 0734.35159 PDFBibTeX XMLCite \textit{P. I. Plotnikov} and \textit{V. N. Starovoĭtov}, Differ. Equations 29, No. 3, 1 (1993; Zbl 0802.35165); translation from Differ. Uravn. 29, No. 3, 461--471 (1993)