Well-posedness of the generalized Korteweg-de Vries-Burgers equation with nonlinear dispersion and nonlinear dissipation

Nabil Bedjaoui (1) , Joaquim M.C. Correia (2, 3) , Youcef Mammeri (1)

1 LAMFA - Laboratoire Amiénois de Mathématique Fondamentale et Appliquée - UMR CNRS 7352
2 DM/IST - Departamento de Matemática [Lisbonne]
3 University of Évora [Portugal]

We prove the well-posedness of the generalized Korteweg-de Vries-Burgers equation with nonlinear dispersion and nonlinear dissipation$$u_t + f(u)_x - \delta g(u_{xx})_x - \varepsilon h(u_{x})_x = 0.$$Contrary to the linear case, the dispersion properties of the free evolution are useless and a vanishing parabolic regularization is then used.

Mots clés: KdV equation; nonlinear dispersion; nonlinear dissipation; Cauchy problem

Domaines: Mathématiques [math]

Nabil Bedjaoui, Joaquim M.C. Correia, Youcef Mammeri. Well-posedness of the generalized Korteweg-de Vries-Burgers equation with nonlinear dispersion and nonlinear dissipation. International Journal of Pure Mathematics , 2015. ⟨hal-01090308⟩