Well-posedness of Korteweg-de Vries-Burgers equation on a finite domain
The authors prove local-in-time well-posedness in the scale of Sobolev spaces of the initial-boundary value problem with nonhomogeneous boundary conditions for the Korteweg-de Vries-Burgers equation on a finite interval. Physical motivations to study such a problem stem from ferroelectricity theory. Then, continuation of solutions to global-in-time ones is proved using classical arguments of nonlinear interpolation (cf. [\textit{J. Bona} and \textit{R. Scott}, Duke Math. J. 43, 87--99 (1976; Zbl 0335.35032)]).
scientific article; zbMATH DE number 6844795