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UDC 519.95

© A. G. Podgayev, 2013

BOUNDARY CONDITION PROBLEM FOR THE KORTVEG-DE VRIES EQUATION WITH ALTERNATING-SIGN FACTOR. III. WEAK SOLUTIONS

The paper deals with final results of studying the initial boundary value problem in a limited area for two cases of the Kortveg-de Vries equation. In the first case equation contains the second order nonlinear term, and in the second case it does not. Here is considered a low smoothness of the initial function. Results on the existence of weak solutions of the equation under study are provided for the case that the second derivative (µ=0) is linear. Uniqueness of regular solution is proved in this article too.

Keywords: weak solution, boundary conditions, solvability, passage to the limit, the Kortveg-de Vries equation.

References:

  1. Podgaev A. G. Kraevaya zadacha dlya uravneniya Kortvega-de Vriza-Byurgersa so znakoperemennym  koeffitsientom. I. // Vestnik TOGU, 2007, ¹4(7),  S.185-198.
  2. Podgaev A. G. Kraevaya zadacha dlya uravneniya Kortvega-de Vriza-Byurgersa so znakoperemennym  koeffitsientom. II. // Vestnik TOGU, 2008, ¹4,  S.9-20.
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  5. Dubinskiy YU.A. Slabaya skhodimost` v nelineynykh ellipticheskikh i parabolicheskikh uravneniyakh, Matem. sb. 67(109), (1965). 609-642.

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