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UDC 519.95

© Podgayev A.G., 2008

Boundary value problem for the Kortewege-de Vries-Burgers equation with an alternating coefficient. 2

The initial boundary value problem for two cases for the Kortewege-de Vries eq-uation is considered. In the first case the equation contains the second order nonlinear term (case a)) and in the second case it does not (case b)). The estimates for the third order and time derivatives for the approximate solution are found. It is shown how from them the conclusions of the theorems about the existence of a regular solution globally in time is derived for the case a. Such a solution locally in time is found for the equation with no the second derivative term and the existence range is given.

References:

  1. Podgaev A. G. Kraevaya zadacha dlya uravneniya Kortvega-de Vriza-Byurgersa so znakoperemennym koeffitsientom. I // Vestnik TOGU. 2007. ¹ 4(7).
  2. Podgaev A. G. Kompaktnost` nekotorykh nelineynykh mnozhestv // Doklady AN SSSR. 1985. T. 285. ¹ 5.
  3. Lions ZH.-L. Nekotorye metody resheniya nelineynykh kraevykh zadach. M., 1972.
  4. Lions J. L. Quelques methodes de resolution les problemes aux limites non linearies. Paris, 1969.
  5. Ladyzhenskaya O. A., Ural`skaya N. N. Lineynye i kvazilineynye uravneniya ellipticheskogo tipa. M., 1973.

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