MR Hironari MIYOSHI and Masayoshi TSUTSUMI Hironari MIYOSHI and Masayoshi TSUTSUMI Convergence of Hydrodynamical Limits for Generalized Carleman Models Funkcialaj Ekvacioj. Serio Internacia 59 2016 351--382 http://fe.math.kobe-u.ac.jp/FE/FullPapers/59-3/59_351.pdf http://www.ams.org/mathscinet-getitem?mr=MR We consider the initial-boundary value problem for a 2-speed system of first order semilinear hyperbolic equations. We establish the existence of global weak solutions in $L^1$ by the theory of nonlinear contraction semigroups. Using the monotone method and the div-curl lemma, we investigate the hydrodynamical limits of the solutions of the hyperbolic systems and show that the limits verify the doubly nonlinear parabolic equations. Carleman's equation, Monotone method, Div-curl lemma, Hydrodynamical limit. 35L50, 37D50. 59-351 2016 Convergence of Hydrodynamical Limits for Generalized Carleman Models Hironari MIYOSHI and Masayoshi TSUTSUMI Hironari MIYOSHI and Masayoshi TSUTSUMI 1 Carleman, T. Problèmes mathématiques dans la théorie cinétique des gaz Publ. Sci. Inst. Mittag-Leffler. 2 Almqvist & Wiksells Boktryckeri Ab, Uppsala 1957 MR0098477 2 Caznave, T.; Haraux, A. An Introduction to Semilinear Evolution Equations Oxford Lecture Series in Mathematics and its Applications, 13, The Clarendon Press, Oxford University Press, New York 1998 MR1691574
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