Higher order for the generalized BBM-burgers equation: existence and convergence results

Abstract

We study the global existence of solutions for certain equations of the form

as δ > 0 and γ _n > 0, n = 1, …, N approach zero, and f is a sufficiently smooth function satisfying certain appropriate assumptions. We consider solutions of hyperbolic conservation laws regularized of these 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

AMS Subject Classifications:

• Primary: 35L65
• Secondary: 76N10

Acknowledgement

Claudete M. Webler was supported by Capes, Brazil.