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Rothe method; non-homogeneous initial and boundary conditions; weak solution

References:

[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. MR 0298237 | Zbl 0217.41601

[2] Kačur J.: **Application of Rothe's Method to Nonlinear Evolution Equations**. Matem. časopis SAV 25 (1975), No 1, 63-81. MR 0394344 | Zbl 0298.34058

[3] Kačur J., Wawruch A.: **On an Approximate Solution for Quasilinear Parabolic Equations**. Czech. Math. J. 27 (102), 1977, 220-241. MR 0605665

[4] Nečas J.: **Les méthodes directes en théorie aux équations elliptiques**. Praha, Akademia 1967.