A non-homogeneous boundary-value problem for the Korteweg-de Vries equation in a quarter plane

By Jerry L. Bona, S. Sun, Bingyu Zhang. 2001

175 citations recorded by the source corpus.

Subfields: Computational Mechanics, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/59474b45a273ff51d7c3d7de97b697cc8d1d9079

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In Computational Mechanics

In Mathematical Physics

In Statistical and Nonlinear Physics

Citations in the corpus

Sharp well-posedness results for the BBM equation (2008, background): “Much effort has been expended on various aspects of the pure initial value problems ut + ux + uux + uxxx = 0 (1) or ut + ux + uux − uxxt = 0 (2) with u(x, 0) = u0(x), (3) though these are not always the most physically relevant formulations (see the discussions in [3], [4], [5] [8], [10]).”
The Initial-Boundary Value Problem for the Korteweg–de Vries Equation (2005, methodology): “Surveys of the literature are given in Bona et al. (2002, 2003) and Colliander and Kenig (2002). Here, we briefly mention some of the more recent contributions. The problem (1.5), (1.10) for s ≥ 0 is treated in Bona et al. (2003) and (1.1) (1.8) for s > 3 4 in Bona et al. (2002) by a Laplace transfo”
THE GENERALIZED KORTEWEG–DE VRIES EQUATION ON THE HALF LINE (2001, methodology): “A recent preprint of Bona, Sun and Zhang ([1]) uses a Laplace transform technique in the framework of function spaces developed in [19] to treat the k = 1 version of the right half-line problem (1.1) with transport term for initial data φ ∈ Hs(R+) and boundary data f ∈ H(s+1)/3(R+) provided s > 3/4.”
An Initial Boundary-Value Problem in a Half-Strip for the Korteweg–De Vries Equation in Fractional-Order Sobolev Spaces (2005, methodology): “In the paper Bona et al. (2002) the problem was studied for a = 1, f ≡ 0. The boundary potential J1 for Eq. (1.10) (when a = 1) was constructed by another method, than in Faminskii (1999b), namely by means of the Laplace transform. With the use of ideas of nonlinear interpolation global well-posedne”