| D. Donatelli and P. Marcati, Convergence of singular limits for multi-d semilinear hyperbolic systems to parabolic systems, Tech. Report 12, Scuola Normale Superiore, Pisa, 2000. |
....its parabolic behavior time asymptotically. Among all, in this contest, we recall the papers of Kurtz [Kur73] and McKean [McK75] where for the rst time this feature for hyperbolic systems has been put into evidence. Afterwards, we recall the papers of Marcati with various collaborators (see [MR00, DM00] and the references therein) where the above scaling has been used for di erent systems and the convergence has been obtained for weak solutions with the aid of the compensated compactness. Moreover, we recall the paper of Lions and Toscani [LT97] where the same parabolic behavior has been ....
D. Donatelli and P. Marcati, Convergence of singular limits for multi-d semilinear hyperbolic systems to parabolic systems, Tech. Report 12, Scuola Normale Superiore, Pisa, 2000.
.... [10] and McKean [19] this scaling has also been systematically used in the analysis of hyperbolic parabolic relaxation limits for weak solutions of hyperbolic systems of balance laws with strongly di usive source terms by means of compensated compactness techniques by Marcati and collaborators [17, 16, 18, 6]. For other di usive kinetic models and approximations, we refer to [14, 12, 11] A general class of kinetic approximations for (possibly degenerate) parabolic equations in multi D has been considered in [4, 1] Let us also point out that the same scaling was used in [15] to analyze the ....
D. Donatelli and P. Marcati. Convergence of singular limits for multi-D semilinear hyperbolic systems to parabolic systems. Technical Report 12, Scuola Normale Superiore, Pisa, 2000.
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