Convergence of a family of perturbed conservation laws with diffusion and non-positive dispersion

We consider a family of conservation laws with convex flux perturbed by vanishing diffusion and non-positive dispersion of the form ut+f(u)x=εuxx−δ(|uxx|n)x. Convergence of the solutions {uε,δ} to the entropy weak solution of the hyperbolic limit equation ut+f(u)x=0, for all real numbers 1≤n≤2 is pr...

Full description

Saved in:
Bibliographic Details
Published in:Nonlinear analysis 2020-03, Vol.192, p.111701, Article 111701
Main Authors: Bedjaoui, N., Correia, J.M.C., Mammeri, Y.
Format: Article
Language:English
Subjects:
Conservation laws
Convergence
Diffusion
Dispersion
Entropy measure-valued solutions
Entropy of solution
Hyperbolic conservation laws
KdV–Burgers equation
Mathematics
Nonlinear dispersion
Real numbers
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We consider a family of conservation laws with convex flux perturbed by vanishing diffusion and non-positive dispersion of the form ut+f(u)x=εuxx−δ(|uxx|n)x. Convergence of the solutions {uε,δ} to the entropy weak solution of the hyperbolic limit equation ut+f(u)x=0, for all real numbers 1≤n≤2 is proved if δ=o(ε3n−12;ε5n−12(2n−1)).
ISSN:0362-546X
1873-5215
DOI:10.1016/j.na.2019.111701