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Title: On a limit of perturbed conservation laws with saturating diffusion and non-positive dispersion
Authors: Bedjaoui, Nabil
Correia, Joaquim M.C.
Mammeri, Youcef
Editors: Kaspar Nipp
Keywords: Saturating diffusion
Nonlinear dispersion
KdV–Burgers equation
Hyperbolic conservation laws
Entropy measure-valued solutions
Issue Date: 9-Mar-2020
Publisher: Springer Nature Switzerland AG, Zeitschrift fur angewandte Mathematik und Physik (ZAMP)
Citation: N. Bedjaoui, J. M. C. Correia and Y. Mammeri, On a limit of perturbed conservation laws with saturating diffusion and non-positive dispersion, Z. Angew. Math. Phys. (2020) 71:59
Abstract: We consider a conservation law with convex flux, perturbed by a saturating diffusion and non-positive dispersion of the form $u_t + f(u)_x = ε(u_x/\sqrt{1+u_x^2})_x − δ(|u_xx|^n)_x$. We prove the convergence of the solutions $u^{ε,δ}$ to the entropy weak solution of the hyperbolic conservation law, $u_t + f(u)_x = 0$, for all real number $1 ≤ n ≤ 2$ provided $δ = o(ε^{n(n+1)/2};ε^{n+1/n})$.
Type: article
Appears in Collections:CIMA - Publicações - Artigos em Revistas Internacionais Com Arbitragem Científica

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