Global Well-posedness and Asymptotic Behavior of a Class of Initial-Boundary-Value Problem of the Korteweg-de Vries Equation on a Finite Domain

Details Global Well-posedness and Asymptotic Behavior of a Class of Initial-Boundary-Value Problem of the Korteweg-de Vries Equation on a Finite Domain Global Well-posedness and Asymptotic Behavior of a Class of Initial-Boundary-Value Problem of the Korteweg-de Vries Equation on a Finite Domain

2010-10-22

arxiv.org/abs/1010.4658v1

Mathematics

Analysis of PDEs

23 pages

Scientific paper

In this paper, we study a class of initial boundary value problem (IBVP) of the Korteweg- de Vries equation posed on a ?nite interval with nonhomogeneous boundary conditions. The IBVP is known to be locally well-posed, but its global $L^2 $ a priori estimate is not available and therefore it is not clear whether its solutions exist globally or blow up in finite time. It is shown in this paper that the solutions exist globally as long as their initial value and the associated boundary data are small, and moreover, those solutions decay exponentially if their boundary data decay exponentially

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