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Inverse Problems in Science and Engineering Volume 19, 2011 - Issue 5: Proceedings of the 5th International Conference on Inverse Problems: Modeling and Simulation, May 24th-29th, 2010, held in Antalya, Turkey
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Original Articles

Semilinear parabolic problems with nonlocal Dirichlet boundary conditions

M. SlodičkaDepartment of Mathematical Analysis, Faculty of Engineering and Architecture, Ghent University, Galglaan 2, Ghent, B-9000, Belgium
Pages 705-716 | Received 16 Mar 2011, Accepted 26 Mar 2011, Published online: 13 Jul 2011

References

  • Cohn, S, Pfabe, K, and Redepenning, J, 1999. A similarity solution to a problem in nonlinear ion transport with a nonlocal condition, Math. Models Methods Appl. Sci. 9 (3) (1999), pp. 445–461.
  • Dehghan, M, 2003. On the numerical solution of the diffusion equation with a nonlocal boundary condition, Math. Probl. Eng. 2003 (2) (2003), pp. 81–92.
  • Hasanov, A, Pektas, B, and Hasanoglu, S, 2009. An analysis of nonlinear ion transport model including diffusion and migration, J. Math. Chem. 46 (4) (2009), pp. 1188–1202.
  • Day, WA, 1982. Extensions of a property of the heat equation to linear thermoelasticity and other theories, Q. Appl. Math. 40 (1982), pp. 319–330.
  • Day, WA, 1983. A decreasing property of solutions of parabolic equations with applications to thermoelasticity, Q. Appl. Math. 41 (1983), pp. 468–475.
  • Friedman, A, 1986. Monotonic decay of solutions of parabolic equations with nonlocal boundary conditions, Q. Appl. Math. 44 (1986), pp. 401–407.
  • Kawohl, B, 1987. Remarks on a paper by W.A. Day on a maximum principle under nonlocal boundary conditions, Q. Appl. Math. 44 (1987), pp. 751–752.
  • Ekolin, G, 1991. Finite difference methods for a nonlocal boundary value problem for the heat equation, BIT 31 (2) (1991), pp. 245–261.
  • Lin, Y, Xu, S, and Yin, H-M, 1997. Finite difference approximations for a class of nonlocal parabolic equations, Int. J. Math. Math. Sci. 20 (1) (1997), pp. 147–163.
  • Liu, Y, 1999. Numerical solution of the heat equation with nonlocal boundary conditions, J. Comput. Appl. Math. 110 (1) (1999), pp. 115–127.
  • Sun, Z-Z, 2001. A high-order difference scheme for a nonlocal boundary-value problem for the heat equation, Comput. Methods Appl. Math. 1 (4) (2001), pp. 398–414.
  • Borovykh, N, 2002. Stability in the numerical solution of the heat equation with nonlocal boundary conditions, Appl. Numer. Math. 42 (1–3) (2002), pp. 17–27.
  • Sapagovas, M, 2002. Hypothesis on the solvability of parabolic equations with nonlocal conditions, Nonlinear Anal., Model. Control 7 (1) (2002), pp. 93–104.
  • Amosov, AA, 2005. Global Solvability of a Nonlinear Nonstationary Problem with a nonlocal boundary condition of radiative heat transfer type, Differ. Equ. 41 (1) (2005), pp. 96–109.
  • Carl, S, and Lakshmikantham, V, 2002. Generalized quasilinearization method for reaction–diffusion equations under nonlinear and nonlocal flux conditions, J. Math. Anal. Appl. 271 (1) (2002), pp. 182–205.
  • Slodička, M, and Dehilis, S, 2009. A numerical approach for a semilinear parabolic equation with a nonlocal boundary condition, J. Comput. Appl. Math. 231 (2009), pp. 715–724.
  • Slodička, M, and Dehilis, S, 2010. A nonlinear parabolic equation with a nonlocal boundary term, J. Comput. Appl. Math. 233 (12) (2010), pp. 3130–3138.
  • Pao, CV, 2001. Numerical solutions of reaction-diffusion equations with nonlocal boundary conditions, J. Comput. Appl. Math. 136 (1–2) (2001), pp. 227–243.
  • Kačur, J, 1985. "Method of Rothe in Evolution Equations". In: Teubner Texte zur Mathematik.. Vol. 80. Leipzig: Teubner; 1985.
  • Nečas, J, 1967. Les Méthodes Directes en Théorie des Équations Elliptiques.. Prague: Academia; 1967.

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