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Applicable Analysis
An International Journal
Volume 95, 2016 - Issue 6
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Articles

Direct and inverse problem for the parabolic equation with initial value and time-dependent boundaries

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Pages 1307-1326 | Received 30 Apr 2015, Accepted 16 Jun 2015, Published online: 08 Jul 2015

References

  • Byrne HM, Chaplain MAJ. Growth of nonnecrotic tumours in the presence and absence of inhibitors. Math. Biosci. 1995;130:151–181.
  • Byrne HM, Chaplain MAJ. Growth of necrotic tumours in the presence and absence of inhibitors. Math. Biosci. 1996;135:187–216.
  • Burton AC. Rate of growth of solid tumours as a problem of diffusion growth. J. Math. Biol. 1966;30:157–176.
  • Friedman A, Reitich F. Analysis of a mathematical model for the growth of tumours. J. Math. Biol. 1999;38:262–284.
  • Greenspan HP. Models for the growth of a solid tumour by diffusion. Stud. Appl. Math. 1972;52:317–340.
  • Xu Y, Gilbert R. Some inverse problems raised from a mathematical model of ductal carcinoma in situ. Math. Comput. Model. 2009;49:814–828.
  • Xu Y. A free boundary problem model of ductal carcinoma in situ. Discrete Contin. Dyn. Syst. Ser. B. 2004;4:337–348.
  • Xu Y. A mathematical model of ductal carcinoma in situ and its characteristic stationary solutions. In: Begehr H, et al., editors. Advances in analysis. World Scientific; 2005.
  • Xu Y. A free boundary problem of diffusion equation with integral condition. Appl. Anal. 2006;85:1143–1152.
  • Xu Y. A free boundary problem of parabolic complex equation. Complex Var. Elliptic Equ. 2006;51:945–951.
  • Xu Y. An inverse problem for the free boundary model of ductal carcinoma in situ. In: Begehr H, Nicolosi F, editors. More progresses in analysis. World Science Publisher; 2008. p. 1429–1438.
  • Cannon JR, Lin Y, Wang S. Determination of source parameter in parabolic equations. Meccanica. 1992;27:85–94.
  • Dehghan M. Finding a control parameter in one-dimensional parabolic equations. Appl. Math. Comput. 2003;130:491–503.
  • Dehghan M. Parameter determination in a partial differential equation from the overspecified data. Math. Comput. Model. 2005;41:196–213.
  • Tatari M, Dehghan M, Razzaghi M. Determination of a time-dependent parameter in a one-dimensional quasi-linear parabolic equation with temperature overspecification. Int. J. Comput. Math. 2006;83:905–913.
  • Kress R. Linear integral equations. New York (NY): Springer-Verlag; 1989. p. 134–141.
  • Friedman A. Partial differential equations of parabolic type. Englewood Cliffs (NJ): Prentice-Hall; 1964. p. 7–13.
  • Hackbusch W. Integral equations: theory and numerical treatment. Boston (MA): Springer Science and Business Media; 1995 Jun 1. p. 25–26.
  • Becker LC, Wheeler M. Numerical and graphical solutions of Volterra equations of the second kind. Maple Application Center; 2005.

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