Well-posedness of the generalized Korteweg-de Vries-Burgers equation with nonlinear dispersion and nonlinear dissipation - Archive ouverte HAL Access content directly
Journal Articles International Journal of Pure Mathematics Year : 2015

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

Abstract

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.
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Dates and versions

hal-01090308 , version 1 (03-12-2014)

Identifiers

  • HAL Id : hal-01090308 , version 1

Cite

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⟩
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