Far Eastern Mathematical Journal

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On the convergence velocity of Rothe's method for parabolic equation in noncylindric domain


P. V. Vinogradova, A. G. Zarubin

2004, issue 1, Ñ. 5–11


Abstract
This article investigates the Rothe's method for starting boundary value problem for the linear parabolic equation of the second order in the domain, the boundary of which depends on time. The estimates of the convergence are obtained.

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References

[1] E. Rothe, “Warmeleiturgsgleichung mit nichtconstanten koeffizienten”, Math. Ann., 104 (1931), 340–362.
[2] P. V. Vinogradova, A. G. Zarubin, “O metode Galerkina dlya kvazilinejnyx parabolicheskix uravnenij v necilindricheskoj oblasti”, Dal'nevost. mat. zhurn., 3:1 (2002), 3–17.
[3] O. A. Ladyzhenskaya, V. A. Solonnikov, N. N. Ural'ceva, Linejnye i kvazilinejnye uravneniya parabolicheskogo tipa, Nauka, M., 1967, 736 s.
[4] O. A. Ladyzhenskaya, N. N. Ural'ceva, Linejnye i kvazilinejnye uravneniya e'llipticheskogo tipa, Nauka, M., 1964, 540 s.
[5] E'. Bekkenbax, R. Bellman, Neravenstva, Mir, M., 1965, 276 s.

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