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PDE’s of evolution; method of Rothe
The aim of this paper is to demonstrate how the variational equations from can be formulated and solved in some abstract Banach spaces without any a priori construction of special linearization schemes. This should be useful e.g. in the analysis of heat conduction problems and modelling of flow in porous media.
[1] L. Čermák: Solution of the problems of Stephan type with convection. Proceedings of the 8-th Seminary on Programs and Algorithms of Numerical Mathematics in Janov nad Nisou (organized by the Mathematical Institute of the Academy of Sciences of the Czech Republic in Prague, in Czech), 1996, pp. 42–49.
[2] J. Dalík, J. Daněček, J. Vala: Numerical solution of the Kiessl model. Appl. Math., to appear. MR 1738893
[3] J. Franců : Monotone operators – a survey directed to differential equations. Appl. Math. 35 (1991), 257–300. MR 1065003
[4] J. Franců : Weakly continuous operators – applications to differential equations. Appl. Math. 39 (1994), 45–56. MR 1254746
[5] S. Fučík, A. Kufner: Nonlinear Differential Equations. Elsevier, Amsterdam, 1980. MR 0558764
[6] H. Gajewski, K. Gröger, K. Zacharias: Nonlinear Operator Equations and Operator Differential Equations. Akademie Verlag, Berlin, 1974. (German) MR 0636412
[7] W. Jäger: On solutions to convection-diffusion equations with degenerate diffusion. PDE’98 Conference in Prague, Book of Abstracts, Appendix, 1998, p. 2.
[8] W. Jäger, J. Kačur: Solution of porous medium type systems by linear approximation schemes. Numerische Mathematik 60 (1991), 407–427. MR 1137200
[9] J. Kačur : Applicaton of relaxation schemes and the method of characteristics to degenerate convection-diffusion problems by a linear approximation scheme. PDE’98 Conference in Prague, Book of Abstracts, 1998, p. 22.
[10] J. Kačur: Method of Rothe in Evolution Equations. Teubner Verlag, Leipzig, 1985. MR 0834176
[11] J. Kačur: Solution to strongly nonlinear parabolic problem by a linear approximation scheme. Preprint M2-96, Comenius University (Faculty of Mathematics and Physics), Bratislava, 1996. MR 1670689
[12] A. Kufner, O. John, S. Fučík: Function Spaces. Academia, Prague, 1977. MR 0482102
[13] V. G. Maz’ya : Sobolev Spaces. Leningrad University Press, Leningrad (St. Petersburg), 1985. (Russian) MR 0817985
[14] J. Nagy, E. Nováková, M. Vacek: Lebesgue Measure and Integral. SNTL, Prague, 1985. (Czech)
[15] K. Yosida: Functional Analysis. Mir, Moscow, 1967. (Russian) MR 0225130 | Zbl 0152.32102
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