Abstract
In this paper, we study an initial-boundary value problem of the Korteweg-de Vries equation posed on a bounded interval $(0,L)$ with nonhomogeneous boundary conditions, which is known to be locally well-posed in the Sobolev space $H^s(0,L)$ with $s\gt-3/4$. Taking the advantage of the hidden dissipative mechanism and the sharp trace regularities of its solutions, we show that the problem is locally well-posed in the space $H^s(0,L)$ with $s\gt-1$.
Citation
Chaohua Jia. Ivonne Rivas. Bing-Yu Zhang. "Lower regularity solutions of a class of non-homogeneous boundary value problems of the Korteweg-de Vries equation on a finite domain." Adv. Differential Equations 19 (5/6) 559 - 584, May/June 2014. https://doi.org/10.57262/ade/1396558061
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