The generalized BBM-Burger equations with non-linear dissipative term: existence and convergence results

Authors: Kondo, Cezar; Webler, Claudete

Source: Applicable Analysis, Volume 87, Number 9, September 2008 , pp. 1085-1101(17)

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Abstract:

We study the global existence of solutions for certain equations of the form ut + f(u)x = γB(ux)x + δuxxt - αuxxxx, as γ > 0, δ > 0 and α > 0 aproach zero, and f and B are sufficiently smooth functions satisfying certain appropriate assumptions. We consider solutions of hyperbolic conservation laws regularized of this equations. Following a pioneering work by Schonbek and a work by LeFloch and Natalini, we establish the convergence of the regularized solutions towards discontinuous solutions of the hyperbolic conservation law.

Keywords: existence and convergence of the smooth solutions; partial differential equations; dissipative term; hyperbolic conservation law

Document Type: Research article

DOI: http://dx.doi.org/10.1080/00036810802428946

Affiliations: 1: Department of Mathematics, Federal University of Sao Carlos, Sao Carlos, Brazil

Publication date: 2008-09-01

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