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Stefan problem
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==References== {{refbegin}} ===Historical references=== *{{Citation |last = Vuik |first = C. |author-link = Kees Vuik |title = Some historical notes about the Stefan problem |journal = [[Nieuw Archief voor Wiskunde]] |series = 4e serie |volume = 11 |issue = 2 |pages = 157–167 |year = 1993 |mr = 1239620 |zbl = 0801.35002 |bibcode = 1993STIN...9332397V }}. An interesting historical paper on the early days of the theory; a [[preprint]] version (in [[PDF]] format) is available here [http://ta.twi.tudelft.nl/nw/users/vuik/wi1605/opgave1/stefan.pdf]. ===Scientific and general references=== *{{Citation |last = Cannon |first = John Rozier |author-link = John Rozier Cannon |title = The One-Dimensional Heat Equation |place = [[Reading, Massachusetts|Reading]]–[[Menlo Park, California|Menlo Park]]–[[London]]–[[Don Mills]]–[[Sydney]]–[[Tokyo]]/ [[Cambridge]]–[[New York City]]–[[New Rochelle]]–[[Melbourne]]–[[Sydney]] |publisher = [[Addison–Wesley|Addison-Wesley Publishing Company]]/[[Cambridge University Press]] |year = 1984 |series = Encyclopedia of Mathematics and Its Applications |volume = 23 |edition = 1st |pages = XXV+483 |url = https://books.google.com/books?id=XWSnBZxbz2oC |mr = 0747979 |zbl = 0567.35001 |isbn =978-0-521-30243-2 }}. Contains an extensive bibliography, 460 items of which deal with the Stefan and other [[free boundary problem]]s, updated to 1982. *{{Citation |last = Kirsch |first = Andreas |title = Introduction to the Mathematical Theory of Inverse Problems |place = Berlin–Heidelberg–New York |publisher = [[Springer Verlag]] |year = 1996 |series= Applied Mathematical Sciences series |volume = 120 |pages = x+282 |url = https://books.google.com/books?id=llNUaSKHj3gC |mr = 1479408 |zbl = 0865.35004 |isbn = 0-387-94530-X}} *{{Citation |last = Meirmanov |first = Anvarbek M. |author-link = Anvarbek Meirmanov |title = The Stefan Problem |place = Berlin – New York |publisher = [[Walter de Gruyter]] |year = 1992 |series = De Gruyter Expositions in Mathematics |volume = 3 |pages = x+245 |url = https://books.google.com/books?id=ae1VlQjOtJQC |doi = 10.1515/9783110846720 |mr = 1154310 |zbl = 0751.35052 |isbn = 3-11-011479-8}}. {{subscription required|via=[[De Gruyter]]}} An important monograph from one of the leading contributors to the field, describing his proof of the existence of a [[classical solution]] to the multidimensional Stefan problem and surveying its historical development. *{{Citation |last = Oleinik |first = O. A. |author-link = Olga Arsenievna Oleinik |title = A method of solution of the general Stefan problem |journal = [[Proceedings of the USSR Academy of Sciences|Doklady Akademii Nauk SSSR]] |language = ru |volume = 135 |pages = 1050–1057 |year = 1960 |mr = 0125341 |zbl = 0131.09202 }}. The paper containing Olga Oleinik's proof of the existence and uniqueness of a [[generalized solution]] for the [[Dimension|three-dimensional]] Stefan problem, based on previous researches of her pupil [[S.L. Kamenomostskaya]]. *{{Citation |last = Kamenomostskaya |first = S. L. |author-link = Shoshana Kamin |title = On Stefan Problem |journal = Nauchnye Doklady Vysshey Shkoly, Fiziko-Matematicheskie Nauki |volume = 1 |issue = 1 |pages = 60–62 |year = 1958 |language = ru |zbl = 0143.13901 }}. The earlier account of the research of the author on the Stefan problem. *{{Citation |last = Kamenomostskaya |first = S. L. |author-link = Shoshana Kamin |title = On Stefan's problem |journal = [[Matematicheskii Sbornik]] |language = ru |volume = 53(95) |issue = 4 |pages = 489–514 |year = 1961 |url = http://mi.mathnet.ru/eng/msb/v95/i4/p489 |mr = 0141895 |zbl = 0102.09301 }}. In this paper the author proves the existence and uniqueness of a [[generalized solution]] for the [[Dimension|three-dimensional]] Stefan problem, later improved by her master Olga Oleinik. *{{citation |last=Rodrigues |first=J. F. |chapter=The Stefan problem revisited |pages=129–190 |title=Mathematical Models for Phase Change Problems |location= |publisher=Birkhäuser |year=1989 |isbn=0-8176-2309-4 }} *{{Citation |last = Rubinstein |first = L. I. |title = The Stefan Problem |place = [[Providence, R.I.]] |publisher = [[American Mathematical Society]] |year = 1971 |series = Translations of Mathematical Monographs |volume = 27 |pages = viii+419 |url = https://books.google.com/books?id=lDnLwUyiGAwC |mr = 0351348 |zbl = 0219.35043 |isbn = 0-8218-1577-6}}. A comprehensive reference, written by one of the leading contributors to the theory, updated up to 1962–1963 and containing a bibliography of 201 items. *{{Citation |last = Tarzia |first = Domingo Alberto |title = A Bibliography on Moving-Free Boundary Problems for the Heat-Diffusion Equation. The Stefan and Related Problems |journal = MAT. Serie A: Conferencias, Seminarios y Trabajos de Matemática |volume = 2 |pages = 1–297 |date=July 2000 |issn = 1515-4904 |mr = 1802028 |zbl = 0963.35207 |doi = 10.26422/MAT.A.2000.2.tar |doi-access = free }}. The impressive personal bibliography of the author on moving and free boundary problems (M–FBP) for the heat-diffusion equation (H–DE), containing about 5900 references to works appeared on approximately 884 different kinds of publications. Its declared objective is trying to give a comprehensive account of the existing western mathematical–physical–engineering literature on this research field. Almost all the material on the subject, published after the historical and first paper of Lamé–Clapeyron (1831), has been collected. Sources include scientific journals, symposium or conference proceedings, technical reports and books. {{refend}}
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