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

• Author(s): Bedjaoui, Nabil ; Correia, Joaquim M.C. ; Mammeri, Youcef
• Date: 2020
• Persistent ID: http://hdl.handle.net/10174/26655
• Origin: Repositório Científico da Universidade de Évora
• Subject(s): Diffusion; Nonlinear dispersion; KdV–Burgers equation; Hyperbolic conservation laws; Entropy measure-valued solutions
• Document Type: Journal article
• Language: English

Description

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_xx − δ(|u_xx|^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^(3n−1)/2 ; ε^(5n−1)/2(2n−1) ).