Shoshana Kamin

Shoshana Kamin
Born	December 24, 1930[1] Moscow
Nationality	Israeli
Institutions	Moscow University Tel Aviv University
Alma mater	Moscow University
Doctoral advisor	Olga Arsenievna Oleinik
Known for	Stefan problem partial differential equations elliptic differential equations parabolic partial differential equations

Shoshana Kamin (Russian: Шошана Камин, Hebrew: פרופ' שושנה קמין‎) (born December 24, 1930),^[1] born Susanna L'vovna Kamenomostskaya (Russian: Сусанна Львовна Каменомостская),^[1][2] is a Soviet-born Israeli mathematician, working on the theory of parabolic partial differential equations and related mathematical physics problems.

Biography and work

Shoshana Kamin graduated from Moscow University in 1953 and earned her "candidate of science" degree from the same university in 1959,^[1] under the supervision of Olga Oleinik.^[3] She left the Soviet Union in the early 1971 , becoming professor in Tel Aviv University,^[4] where she is now professor emeritus.^[5]

In the late 1950s, she gave the first proof of the existence and uniqueness of the generalized solution of the three-dimensional Stefan problem.^[6] Her proof was generalised by Oleinik.^[7]

Later, she made important contributions to the study of the porous medium equation,^[8]

$\partial_t u = \Delta_x u^m, \,\, m > 1, \,$

and to non-linear elliptic equations.^[9]

Selected Publications

• Kamenomostskaya, S. L. (1958), "On Stefan Problem", Nauchnye Doklady Vysshey Shkoly, Fiziko-Matematicheskie Nauki (in Russian) 1 (1): 60–62, Zbl 0143.13901. The earlier account of the research of Shoshana Kamin on the Stefan problem.
• Kamenomostskaya, S. L. (1961), "On Stefan's problem", Matematicheskii Sbornik (in Russian), 53(95) (4): 489–514, MR 0141895, Zbl 0102.09301. In this paper and in the paper (Oleinik 1960), the first existence and uniqueness proofs for the generalized solution of the three-dimensional Stefan problem are given.
• Kamenomostskaya, S. L. (March 1973), "The asymptotic behaviour of the solution of the filtration equation", Israel Journal of Mathematics 14 (1): 76–87, doi:10.1007/BF02761536, MR 0315292, Zbl 0254.35054.
• Kamin, S. (June 1976), "Similar solutions and the asymptotics of filtration equations", Archive for Rational Mechanics and Analysis 60 (2): 171–183, doi:10.1007/BF00250678, MR 0397202, Zbl 0336.76036. According to Vázquez (2007, p. 15) this is one of the most important papers in the asymptotic theory of the porous medium equation. Also, perhaps for the last time ever, she signed this work with both her present and former surnames, precisely writing "S. Kamin (Kamenomostskaya)".

See also

• Parabolic partial differential equation
• Refusenik
• Stefan problem

Notes

1. See reference (Fomin & Shilov 1969, p. 562).
2. See her paper (Kamin 1976, p. 171) and her author page at All-Russian Mathematical Portal.
3. See the list of Olga Oleinik Candidate of Sciences students in (Venttsel' et al. 2003, p. 171) (Russian version).
4. See Milman (2006, p. 217). He precisely states:-"The emigration of the mid-1970s had already brought mathematicians of the highest caliber and of all ages to Israel: Mikhail Lifshits and David Milman, Israel Gohberg and Il'ya Pyatetskii-Shapiro, Shoshana Kamin, Boris Moishezon, Yurii Gurevich and I (I include myself in this group)."
5. "List of senior faculty members at the School of Mathematical Sciences". Tel Aviv University.
6. See references (Kamenomostskaya 1961) and (Oleinik 1960), as well as the historical survey on the Stefan problem in (Rubinstein 1969, pp. 1–15).
7. See Oleinik (1960) and Rubinstein (1969, pp. 1–15 and 310).
8. See Vázquez (2007, p. 15).
9. See Rădulescu (2007, p. 22).

References

Biographical references

• Fomin, S. V.; Shilov, G. E., eds. (1969), Математика в СССР 1958–1967 (in Russian), Том второй: Биобиблиография выпуск первый А–Л, Москва: Издательство "Наука", p. 816, MR 0250816, Zbl 0199.28501. The "Mathematics in the USSR 1958–1967" is a two–volume continuation of the opus "Mathematics in the USSR during its first forty years 1917–1957" and describes the developments of Soviet mathematics during the period 1958–1967. Precisely it is meant as a continuation of the second volume of that work and, as such, is titled "Biobibliography" (evidently an acronym of biography and bibliography). It includes new biographies (when possible, brief and complete) and bibliographies of works published by new Soviet mathematicians during that period, and updates on the work and biographies of scientist included in the former volume, alphabetically ordered with respect to author's surname.
• Milman, V. D. (2006), "Observations on the movement of people and ideas in twentieth-century mathematics", in Bolibruch, A. A.; Osipov, Yu. S.; Sinai, Ya. G., Mathematical Events of the Twentieth Century, Berlin-Heidelberg-New York / Moscow: Springer-Verlag / PHASIS, p. 215, ISBN 978-3-540-23235-3, MR 2179060, Zbl 1092.01015
• Venttsel', T. D.; Vladimirov, V. S.; Zhikov, V. V.; Il'in, A. M.; Il'in, V. P.; Kondrat'ev, V. A.; Kudryavtsev, L. D.; Mishchenko, E. F.; Nikol'skii, S. M.; Osipov, Yu. S.; Radkevich, E. V.; Rozov, N. Kh.; Sadovnichii, V. A.; Faddeev, L. D.; Chechkin, G. A.; Shamaev, A. S.; Shaposhnikova, T. A.; Shkalikov, A. A. (2003), "Ol'ga Arsen'evna Oleinik (obituary)", Uspekhi Matematicheskikh Nauk (in Russian) 58 (1(349)): 165–174, MR 1992133, Zbl 1050.01527. An almost comprehensive obituary article: its English translation is published in the Russian Mathematical Surveys as "Ol'ga Arsen'evna Oleinik", Russian Mathematical Surveys 58 (1), 2003: 161–172, doi:10.1070/RM2003v058n01ABEH000607, MR 1992133, Zbl 1050.01527.

Scientific references

• Ladyženskaja, O. A.; Solonnikov, V. A.; N. N., Ural'ceva (1968), Linear and quasi-linear equations of parabolic type, Translations of Mathematical Monographs 23, Providence, RI: American Mathematical Society, pp. XI+648, MR 0241821, Zbl 0174.15403.
• Oleinik, O. A. (1960), "A method of solution of the general Stefan problem", Doklady Akademii Nauk SSSR (in Russian) 135: 1050–1057, Zbl 0131.09202.
• Meirmanov, Anvarbek M. (1992), The Stefan Problem, De Gruyter Expositions in Mathematics 3, Berlin-New York: Walter de Gruyter, pp. x+245, ISBN 3-11-011479-8, MR 1154310, Zbl 0751.35052.
• Rădulescu, Vicenţiu D. (2007). "Singular Phenomena in Nonlinear Elliptic Problems: From Blow-Up Boundary Solutions to Equations with Singular Nonlinearities". In M. Chipot. Handbook of Differential Equations: Stationary Partial Differential Equations 4. North-Holland. pp. 485–593. doi:10.1016/S1874-5733(07)80010-6. ISBN 978-0-444-53036-3. MR 2569336. Zbl 1193.35053..
• Rubinstein, L. I. (1971), The Stefan Problem, Translations of Mathematical Monographs 27, Providence, R.I.: American Mathematical Society, pp. viii+419, ISBN 0-8218-1577-6, MR 0351348, Zbl 0219.35043. A comprehensive reference updated up to 1962–1963, with a bibliography of 201 items, including also a paragraph of 15 pages sketching the history of the subject
• Vázquez, Juan Luis (2007). The porous medium equation. Mathematical theory. Oxford Mathematical Monographs. Oxford: The Clarendon Press, Oxford University Press. pp. xxii+624. ISBN 978-0-19-856903-9. MR 2286292. Zbl 1107.35003.

External links

• Shoshana Kamin at the Mathematics Genealogy Project