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Title: Convergence of a family of perturbed conservation laws with diffusion and non-positive dispersion
Authors: Bedjaoui, Nabil
Correia, Joaquim M.C.
Mammeri, Youcef
Editors: Radulescu, Vicentiu
Valdinoci, Enrico
Keywords: Diffusion
Nonlinear dispersion
KdV–Burgers equation
Hyperbolic conservation laws
Entropy measure-valued solutions
Issue Date: Mar-2020
Publisher: Elsevier, Nonlinear Analysis
Citation: N. Bedjaoui, J.M.C. Correia, Y. Mammeri, Convergence of a family of perturbed conservation laws with diffusion and non-positive dispersion, Nonlinear Analysis 192 (2020) 111701
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_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) ).
Type: article
Appears in Collections:CIMA - Publicações - Artigos em Revistas Internacionais Com Arbitragem Científica

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