Bougoffa, Lazhar; Rach, Randolph C.; Mennouni, Abdelaziz On the existence, uniqueness, and new analytic approximate solution of the modified error function in two-phase Stefan problems. (English) Zbl 1472.35463 Math. Methods Appl. Sci. 44, No. 14, 10948-10956 (2021). MSC: 35R35 80A22 34B15 34B08 PDF BibTeX XML Cite \textit{L. Bougoffa} et al., Math. Methods Appl. Sci. 44, No. 14, 10948--10956 (2021; Zbl 1472.35463) Full Text: DOI OpenURL
Bollati, Julieta; Semitiel, Jose A.; Natale, Maria F.; Tarzia, Domingo A. Existence and uniqueness of the \(p\)-generalized modified error function. (English) Zbl 1461.34048 Electron. J. Differ. Equ. 2020, Paper No. 35, 11 p. (2020). Reviewer: Alessandro Calamai (Ancona) MSC: 34B18 34B15 47H10 33E30 PDF BibTeX XML Cite \textit{J. Bollati} et al., Electron. J. Differ. Equ. 2020, Paper No. 35, 11 p. (2020; Zbl 1461.34048) Full Text: arXiv Link OpenURL
Ceretani, Andrea N.; Salva, Natalia N.; Tarzia, Domingo A. Auxiliary functions in the study of Stefan-like problems with variable thermal properties. (English) Zbl 1439.80009 Appl. Math. Lett. 104, Article ID 106204, 6 p. (2020). Reviewer: Alain Brillard (Riedisheim) MSC: 80A22 35Q79 35A01 35A02 PDF BibTeX XML Cite \textit{A. N. Ceretani} et al., Appl. Math. Lett. 104, Article ID 106204, 6 p. (2020; Zbl 1439.80009) Full Text: DOI arXiv OpenURL
Ceretani, Andrea N.; Salva, Natalia N.; Tarzia, Domingo A. Approximation of the modified error function. (English) Zbl 1427.33001 Appl. Math. Comput. 337, 607-617 (2018). MSC: 33B15 34B08 34B15 35R35 65D20 80A22 PDF BibTeX XML Cite \textit{A. N. Ceretani} et al., Appl. Math. Comput. 337, 607--617 (2018; Zbl 1427.33001) Full Text: DOI arXiv OpenURL
Boldrini, José Luiz; Dias Vaz, Cristina Lúcia Existence and regularity of solutions of a phase field model for solidification with convection of pure materials in two dimensions. (English) Zbl 1034.76057 Electron. J. Differ. Equ. 2003, Paper No. 109, 25 p. (2003). MSC: 76T99 80A22 76R10 76D03 35Q30 35R35 PDF BibTeX XML Cite \textit{J. L. Boldrini} and \textit{C. L. Dias Vaz}, Electron. J. Differ. Equ. 2003, Paper No. 109, 25 p. (2003; Zbl 1034.76057) Full Text: EuDML EMIS OpenURL
Ball, J. M. (ed.); Kinderlehrer, D. (ed.); Podio-Guidugli, P. (ed.); Slemrod, M. (ed.) Fundamental contributions to the continuum theory of evolving phase interfaces in solids. A collection of reprints of 14 seminal papers, dedicated to Morton E. Gurtin on the occasion of his sixty-fifth birthday. (English) Zbl 0968.74003 Berlin: Springer. viii, 474 p. (1999). Reviewer: I.A.Parinov (Rostov-na-Donu) MSC: 74-06 74Nxx 00B30 PDF BibTeX XML Cite \textit{J. M. Ball} (ed.) et al., Fundamental contributions to the continuum theory of evolving phase interfaces in solids. A collection of reprints of 14 seminal papers, dedicated to Morton E. Gurtin on the occasion of his sixty-fifth birthday. Berlin: Springer (1999; Zbl 0968.74003) OpenURL
Danilov, V. G.; Omel’yanov, G. A.; Radkevich, E. V. Justification of asymptotics of solutions of the phase-field equations and a modified Stefan problem. (English. Russian original) Zbl 0870.35127 Sb. Math. 186, No. 12, 1753-1771 (1995); translation from Mat. Sb. 186, No. 12, 63-80 (1995). MSC: 35R35 35C20 35B25 35K55 PDF BibTeX XML Cite \textit{V. G. Danilov} et al., Sb. Math. 186, No. 12, 1753--1771 (1995; Zbl 0870.35127); translation from Mat. Sb. 186, No. 12, 63--80 (1995) Full Text: DOI OpenURL
Omel’yanov, G. A.; Radkevich, E. V.; Danilov, V. G. Stability and ”stabilization” of the solution of phase field system. (English) Zbl 0864.35062 Kenmochi, N. (ed.) et al., Proceedings of the Banach Center minisemester on nonlinear analysis and applications, Warsaw, Poland, November 14 – December 15, 1994. Tokyo: Gakkōtosho Co., Ltd. GAKUTO Int. Ser., Math. Sci. Appl. 7, 319-342 (1995). MSC: 35K85 35K60 35K40 PDF BibTeX XML Cite \textit{G. A. Omel'yanov} et al., GAKUTO Int. Ser., Math. Sci. Appl. 7, 319--342 (1995; Zbl 0864.35062) OpenURL
Danilov, V. G.; Omel’yanov, G. A.; Radkevich, E. V. Asymptotics of the solution to the phase field system and the modified Stefan problem. (English. Russian original) Zbl 0855.35134 Differ. Equations 31, No. 3, 446-454 (1995); translation from Differ. Uravn. 31, No. 3, 483-491 (1995). Reviewer: V.Chernyatin (Szczecin) MSC: 35R35 80A22 PDF BibTeX XML Cite \textit{V. G. Danilov} et al., Differ. Equations 31, No. 3, 446--454 (1995; Zbl 0855.35134); translation from Differ. Uravn. 31, No. 3, 483--491 (1995) OpenURL
Danilov, V. G.; Omel’yanov, G. A.; Radkevich, E. V. A modified Stefan problem as a limit of the asymptotics of a phase field system. (English. Russian original) Zbl 0879.35164 Dokl. Math. 52, No. 1, 74-77 (1995); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 343, No. 5, 586-589 (1995). MSC: 35R35 80A22 PDF BibTeX XML Cite \textit{V. G. Danilov} et al., Dokl. Math. 52, No. 1, 74--77 (1995; Zbl 0879.35164); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 343, No. 5, 586--589 (1995) OpenURL
Radkevich, E. The Gibbs-Thomson effect and existence conditions for classical solutions for the modified Stefan problem. (English) Zbl 0788.35155 Chadam, John M. (ed.) et al., Free boundary problems involving solids. Proceedings of the international colloquium ”Free boundary problems: theory and applications”, held in Montreal, Canada, June 13 - June 22, 1990. Harlow, Essex: Longman Scientific & Technical. Pitman Res. Notes Math. Ser. 281, 135-142 (1993). MSC: 35R35 35K20 80A22 PDF BibTeX XML Cite \textit{E. Radkevich}, in: Free boundary problems involving solids. Proceedings of the international colloquium ''Free boundary problems: theory and applications'', held in Montreal, Canada, June 13 - June 22, 1990. Harlow, Essex: Longman Scientific \& Technical; New York: Wiley. 135--142 (1993; Zbl 0788.35155) OpenURL
Caginalp, G. The issues of anisotropy and travelling wave velocity selection in the phase field model. (English) Zbl 0859.35142 Chadam, John M. (ed.) et al., Free boundary problems involving solids. Proceedings of the international colloquium ”Free boundary problems: theory and applications”, held in Montreal, Canada, June 13 - June 22, 1990. Harlow, Essex: Longman Scientific & Technical. Pitman Res. Notes Math. Ser. 281, 92-95 (1993). Reviewer: L.A.Sakhnovich (Odessa) MSC: 35R35 80A22 PDF BibTeX XML Cite \textit{G. Caginalp}, in: Free boundary problems involving solids. Proceedings of the international colloquium ''Free boundary problems: theory and applications'', held in Montreal, Canada, June 13 - June 22, 1990. Harlow, Essex: Longman Scientific \& Technical; New York: Wiley. 92--95 (1993; Zbl 0859.35142) OpenURL
Bazaliy, B. V.; Degtyarev, S. P. The classical Stefan problem as the limit case of the Stefan problem with a kinetic condition at the free boundary. (English) Zbl 0817.35133 Antontsev, S. N. (ed.) et al., Free boundary problems in continuum mechanics. International conference on free boundary problems in continuum mechanics, Novosibirsk, Russia, July 15-19, 1991. Basel: Birkhäuser. ISNM, Int. Ser. Numer. Math. 106, 83-90 (1992). MSC: 35R35 80A22 PDF BibTeX XML Cite \textit{B. V. Bazaliy} and \textit{S. P. Degtyarev}, ISNM, Int. Ser. Numer. Math. 106, 83--90 (1992; Zbl 0817.35133) OpenURL
Tkebuchava, R. S. Existence and uniqueness of a solution to the Bellman equation in the problem of optimally correcting a Markov process. (Russian. English summary) Zbl 0737.49023 Soobshch. Akad. Nauk Gruz. SSR 141, No. 2, 245-247 (1991). MSC: 49L99 49J20 60G40 PDF BibTeX XML Cite \textit{R. S. Tkebuchava}, Soobshch. Akad. Nauk Gruz. SSR 141, No. 2, 245--247 (1991; Zbl 0737.49023) OpenURL