On a limit of perturbed conservation laws with saturating diffusion and non-positive dispersion

N. Bedjaoui (1) , J. M. C. Correia , Y. Mammeri (1)

1 LAMFA - Laboratoire Amiénois de Mathématique Fondamentale et Appliquée - UMR CNRS 7352

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)=epsilon(u(x)root 1+u(x)(2))(x)-delta(|u(xx)|(n))(x). We prove the convergence of the solutions \u(epsilon,delta)\ to the entropy weak solution of the hyperbolic conservation law, u(t)+f(u)(x)=0, for all real number 1 <= n <= 2 provided delta=o(epsilon(n(n+1)/2);epsilon(n+1/n)).

Domaines: Mathématiques [math]

N. Bedjaoui, J. M. C. Correia, Y. Mammeri. On a limit of perturbed conservation laws with saturating diffusion and non-positive dispersion. Zeitschrift für Angewandte Mathematik und Physik, 2020, 71 (2), ⟨10.1007/s00033-020-1279-8⟩. ⟨hal-03621703⟩