Convergence of a family of perturbed conservation laws with diffusion and non-positive dispersion. (March 2020)

• Record Type: Journal Article
• Authors: Bedjaoui, N.; Correia, J.M.C.; Mammeri, Y.
• Is Part Of: Nonlinear analysis. Volume 192(2020)
• Publication Date: 2020-03
• Subjects: Diffusion -- Nonlinear dispersion -- KdV–Burgers equation -- Hyperbolic conservation laws -- Entropy measure-valued solutions; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2019.111701
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We consider a family of conservation laws with convex flux perturbed by vanishing diffusion and non-positive dispersion of the form u t + f ( u ) x = ε u x x − δ ( | u x x | n ) x . Convergence of the solutions { u ε, δ } to the entropy weak solution of the hyperbolic limit equation u t + f ( u ) x = 0, for all real numbers 1 ≤ n ≤ 2 is proved if δ = o ( ε 3 n − 1 2 ; ε 5 n − 1 2 ( 2 n − 1 ) ) .