A non-homogeneous boundary-value problem for the Korteweg–de Vries equation posed on a finite domain II

By Jerry L. Bona, Shu-Ming Sun, Bingyu Zhang. 2003

146 citations recorded by the source corpus.

Abstract Studied here is an initial- and boundary-value problem for the Korteweg–de Vries equation posed on a bounded interval with nonhomogeneous boundary conditions. This particular problem arises naturally in certain circumstances when the equation is used as a model for waves and a numerical scheme is needed. It is shown here that this initial-boundary-value problem is globally well-posed in the L 2-based Sobolev space H s (0, 1) for any s ≥ 0. In addition, the mapping that associates to appropriate initial- and boundary-data the corresponding solution is shown to be analytic as a function between appropriate Banach spaces.

Subfields: Applied Mathematics, Electrical and Electronic Engineering, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/eecb894354855ef5320d5d3d5da2f09f85562ece

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In Applied Mathematics

In Electrical and Electronic Engineering

In Mathematical Physics

Citations in the corpus

Boundary controllability for the nonlinear Korteweg–de Vries equation on any critical domain (2009, background): “Remark 2.6. In [ 3 ] and [15], one can find some well-posedness results in the case where there are nonhomogeneous Dirichlet boundary conditions.”
On the exponential decay of the critical generalized Korteweg-de Vries equation with localized damping (2007, unknown): “1) (see for instance, [1], [2], [5], [9], [12], [13]).”
Boussinesq equations and other systems for small-amplitude long waves in nonlinear dispersive media: II. The nonlinear theory (2004, methodology): “When such models are used to describe real phenomena, nonhomogeneous boundary conditions imposed at finite spatial positions often intrude just as they do for unidirectional models (see, e.g. [19, 20 ,27,28] and the references therein).”
An Initial Boundary-Value Problem in a Half-Strip for the Korteweg–De Vries Equation in Fractional-Order Sobolev Spaces (2005, background): “Note that initial boundary-value problems in other domains for the KdV equations are studied, for example, in Faminskii (1999a), Holmer (2004), Faminskii (2001a,b), Bona et al. (2003) and Khablov (1979b).”