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