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Title: A note on nonhomogeneous initial and boundary conditions in parabolic problems solved by the Rothe method (English)
Author: Rektorys, Karel
Author: Ludvíková, Marie
Language: English
Journal: Aplikace matematiky
ISSN: 0373-6725
Volume: 25
Issue: 1
Year: 1980
Pages: 56-72
Summary lang: English
Summary lang: Czech
Summary lang: Russian
Category: math
Summary: When solving parabolic problems by the so-called Rothe method (see K. Rektorys, Czech. Math. J. 21 (96), 1971, 318-330 and other authors), some difficulties of theoretical nature are encountered in the case of nonhomogeneous initial and boundary conditions. As a rule, these difficulties lead to rather unnatural additional conditions imposed on the corresponding bilinear form and the initial and boundary functions. In the present paper, it is shown how to remove such additional assumptions in the case of the initial conditions and how to replace them by simpler, more natural assumptions in the case of the boundary conditions. In the last chapter applications and convergence of the Ritz method (or of other direct methods) to approximate solution of the originating elliptic problems is considered. (English)
Keyword: Rothe method
Keyword: non-homogeneous initial and boundary conditions
Keyword: weak solution
MSC: 35K15
MSC: 35K20
MSC: 65N40
MSC: 65N99
idZBL: Zbl 0438.65100
idMR: MR0554091
DOI: 10.21136/AM.1980.103837
Date available: 2008-05-20T18:13:37Z
Last updated: 2020-07-28
Stable URL:
Reference: [1] Rektorys K.: On Application of Direct Variational Methods to the Solution of Parabolic Boundary Value Problems of Arbitrary Order in the Space Variables.Czech. Math. J. 21 (96), 1971, 318-330. Zbl 0217.41601, MR 0298237
Reference: [2] Kačur J.: Application of Rothe's Method to Nonlinear Evolution Equations.Matem. časopis SAV 25 (1975), No 1, 63-81. Zbl 0298.34058, MR 0394344
Reference: [3] Kačur J., Wawruch A.: On an Approximate Solution for Quasilinear Parabolic Equations.Czech. Math. J. 27 (102), 1977, 220-241. MR 0605665
Reference: [4] Nečas J.: Les méthodes directes en théorie aux équations elliptiques.Praha, Akademia 1967.


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