The Initial-Boundary Value Problem for the Korteweg–de Vries Equation
نویسندگان
چکیده
منابع مشابه
Initial-Boundary Value Problems for the Korteweg-de Vries Equation
Exact and approximate solutions of the initial-boundary value problem for the Korteweg-de Vries equation on the semi-infinite line are found. These solutions are found for both constant and time-dependent boundary values. The form of the solution is found to depend markedly on the specific boundary and initial value. In particular, multiple solutions and nonsteady solutions are possible. The an...
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We prove local well-posedness of the initial-boundary value problem for the Korteweg-de Vries equation on right half-line, left half-line, and line segment, in the low regularity setting. This is accomplished by introducing an analytic family of boundary forcing operators.
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In this paper, we consider an initial-boundary value problem for the Kortewegde Vries equation on the negative quarter-plane. The normalized Korteweg-de Vries equation considered is given by uτ + uux + uxxx = 0, x < 0, τ > 0, where x and τ represent dimensionless distance and time respectively. In particular, we consider the case when the initial and boundary conditions are given by u(x, 0) = u...
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Résumé Nous continuons l’étude du problème de Cauchy et aux limites pour l’équation de Korteweg-de Vries initiée dans [9]. On obtient des effets régularisants globaux uniformes par rapport à la longueur de l’intervalle et nous montrons que la solution du problème aux limites converge, lorsque la longueur de l’intervalle tend vers l’infini, vers la solution du problème posé sur le quart de plan ...
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ژورنال
عنوان ژورنال: Communications in Partial Differential Equations
سال: 2006
ISSN: 0360-5302,1532-4133
DOI: 10.1080/03605300600718503