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Journal Articles Communications in Mathematical Sciences Year : 2016

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

Abstract

We consider a conservation law perturbed by a linear diffusion and non-positive dispersion $u_t + f(u)_x = \varepsilon u_{xx} − \delta (|u_{xx}|^n)_x$. We prove the convergence of the previous solution to the entropy weak solution of the hyperbolic conservation law $u_t + f(u)_x = 0$, in both cases $n = 1$ and $n = 2.$
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Dates and versions

hal-01191885 , version 1 (02-09-2015)

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Nabil Bedjaoui, Joaquim M.C. Correia, Youcef Mammeri. On a limit of perturbed conservation laws with diffusion and non-positive dispersion. Communications in Mathematical Sciences, 2016, ⟨10.4310/CMS.2016.v14.n6.a2⟩. ⟨hal-01191885⟩
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