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2015 | 13 | 1 |
Tytuł artykułu

On the smoothness of the free boundary in a nonlocal one-dimensional parabolic free boundary value problem

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We consider one-dimensional parabolic free boundary value problem with a nonlocal (integro-differential) condition on the free boundary. Results on Cm-smoothness of the free boundary are obtained. In particular, a necessary and sufficient condition for infinite differentiability of the free boundary is given.
Wydawca
Czasopismo
Rocznik
Tom
13
Numer
1
Opis fizyczny
Daty
otrzymano
2014-01-22
zaakceptowano
2015-03-18
online
2015-04-01
Twórcy
  • Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Acad. G.
    Bonchev Str., Bl. 8, 1113 Sofia, Bulgaria
Bibliografia
  • [1] N. Bellomo, N. K. Li, P. K. Maini, On the foundations of cancer modelling: selected topics, speculations, and perspectives. Math.Models Methods Appl. Sci. 18 (2008), no. 4, 593–646.[WoS][Crossref]
  • [2] J. R. Cannon, The one-dimensional heat equation, Encyclopedia of Mathematics and its Applications, vol. 23, Addison-Wesley,Menlo Park, 1984.
  • [3] J. R. Cannon and C. D. Hill, On the infinite differentiability of the free boundary in a Stefan problem, J. Math. Anal. Appl. 22(1968), 385–397.[Crossref]
  • [4] J. R. Cannon and M. Primicerio, A two phase Stefan problem: regularity of the free boundary, Ann. Mat. Pure. Appl. 88 (1971),217–228.
  • [5] Chiang Li-Shang, Existence and differentiability of the solution of the two-phase Stefan problem for quasilinear parabolicequations, Chinese Math.–Acta. 7 (1965), 481–496.
  • [6] A. Corli, V. Guidi and M. Primicerio, On a diffusion problem arising in nanophased thin films, Adv. Math. Sci. Appl. 18 (2008), 517–533.
  • [7] S. Cui, A. Friedman, Analysis of a mathematical model of the growth of necrotic tumors, J. Math. Anal. Appl. 255 (2001), 636–677.[Crossref]
  • [8] A. Friedman, Partial Differential Equations of Parabolic Type, Prentice–Hall, Englewood Cliffs, N.J., 1964.
  • [9] A. Friedman, F. Reitich, Analysis of a mathematical model for the growth of tumors, J. Math. Biol. 38 (1999), 262–284.[Crossref]
  • [10] A. Friedman, Mathematical analysis and challenges arising from models of tumor growth. Math. Models Methods Appl. Sci. 17(2007), suppl., 1751–1772.[Crossref][WoS]
  • [11] O. A. Ladyzhenskaja, V. A. Solonnikov and N. N. Ural’ceva, Linear and Quasilinear Equations of Parabolic Type, Translations ofMathematical Monographs, Vol. 23, Amer. Math. Soc., Providence, R.I., 1968.
  • [12] L. I. Rubinstein, The Stefan problem. Translations of Mathematical Monographs, Vol. 27. AMS, Providence, R.I., 1971.
  • [13] D. Schaeffer, A new proof of infinite differentiability of the free boundary in the Stefan problem, J. Diff. Equat. 20 (1976), 266–269.[Crossref]
  • [14] R. Semerdjieva, Global existence of classical solutions for a nonlocal one dimensional parabolic free boundary problem, HoustonJ. Math. 40 (2014), no. 1, 229–253.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_1515_math-2015-0026
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