Well-Posedness of the Generalized Korteweg-de Vries-Burgers Equation with Nonlinear Dispersion and Nonlinear Dissipation - Bedjaoui, Nabil (2016)
We prove the well-posedness of the generalized Korteweg-de Vries-Burgers equation with nonlinear dispersion and nonlinear dissipation ut+f(u)x−δg(uxx)x−εh(ux)x=0. Contrary the linear case, the dispersion properties of the free evolution are useless and a vanishing parabolic regularization is then used.