SIAM Journal on Mathematical Analysis, Volume 52, Issue 2, Page 1864-1883, January 2020.
We consider a class of the first order hyperbolic systems of PDEs that can be written as moments of a kinetic equation. We construct smooth, local solutions to the Cauchy problem using a discrete time, transport-projection splitting algorithm for the dual kinetic density. The method represents an alternative to the methods of G\aarding [Les EDPs Coll. Int. CRNS, 117 (1963), pp. 33--40] and Kato [Arch. Ration. Mech. Anal., 58 (1975), pp. 181--205] for proving the existence of classical solutions of such systems.

中文翻译：

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具有动力学结构的PDE的双曲系统的经典解

SIAM数学分析杂志，第52卷，第2期，第1864-1883页，2020年1月。
我们考虑了一类PDE的一阶双曲系统，可以将其写为动力学方程的矩。我们为双动力学密度使用离散时间，运输-投影分裂算法构造了柯西问题的光滑局部解。该方法代表了G \ aarding [Les EDPs Coll。诠释 CRNS，117（1963），第33--40页]和Kato [拱门。配给。机甲 Anal。，58（1975），pp。181--205]证明了此类系统的经典解的存在。