Well-Posedness of the Generalized Korteweg-de Vries-Burgers Equation with Nonlinear Dispersion and Nonlinear Dissipation

• Author(s): Bedjaoui, Nabil ; Correia, Joaquim ; Mammeri, Youcef
• Date: 2016
• Persistent ID: http://hdl.handle.net/10174/17722
• Origin: Repositório Científico da Universidade de Évora
• Subject(s): KdV-Burgers equation; nonlinear dispersion; nonlinear dissipation; Cauchy problem
• Document Type: Journal article
• Language: English

Description

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.

FCT, UID/MAT/04674/2013