THE TRANSFORMATION METHOD FOR PARABOLIC EQUATIONS AND VARIATIONAL INEQUALITIES IN NON-CYLINDRICAL DOMAINS

A. Kufner (Czech Republic), K. Kuliev (Czech Republic) and G. Kulieva (Czech Republic)

Received July 10, 2007

References:

[1] I. Bock and J. Kačur, Application of Rothe’s method to parabolic variational inequalities, Math. Slovaca 31 (1981), 429-436. [2] J. Dasht, J. Engström, A. Kufner and L.-E. Persson, Rothe’s method for parabolic equations on non-cylindrical domains, Adv. Alg. Anal. 1 (2006), 1-22. [3] J. Kačur, Application of Rothe’s method to nonlinear evolution equations, Czechoslovak Math. J. 25 (1975), 63-81. [4] J. Kačur, Nonlinear Parabolic Boundary Value Problems with the Time Derivatives in the Boundary Conditions, Proceedings Equadiff 4, Springer, 1979. [5] J. Kačur, Application of Rothe’s method to perturbed linear hyperbolic equations and variational inequalities, Czechoslovak Math. J. 34 (1984), 92-106. [6] A. Kufner, O. John and S. Fučík, Function Spaces, Noordhoff International Publishing, Leyden, 1977. [7] K. Kuliev, G. Kulieva, L.-E. Persson and E. K. Essel, Linear parabolic problems with singular coefficients in non-cylindrical domains, Int. J. Appl. Sci., to appear. [8] K. Kuliev, Parabolic problems on non-cylindrical domains – The method of Rothe, University of West Bohemia, Pilsen, 2007. [9] G. Kulieva, Some special problems in elliptic and parabolic variational inequalities, University of West Bohemia, Pilsen, 2007.

Keywords and phrases: parabolic PDEs, numerical methods, time-discretization, method of lines, transformation method, variational inequality.