Rothe method; non-homogeneous initial and boundary conditions; weak solution
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.
 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. MR 0298237
| Zbl 0217.41601
 Kačur J.: Application of Rothe's Method to Nonlinear Evolution Equations
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| Zbl 0298.34058
 Kačur J., Wawruch A.: On an Approximate Solution for Quasilinear Parabolic Equations
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 Nečas J.: Les méthodes directes en théorie aux équations elliptiques. Praha, Akademia 1967.