Ukrainian Mathematical Bulletin

Volume 1, Issue 4, 2004 pp. 553-568.

On the Kinetic Formulation of First-Order Hyperbolic Quasilinear Systems

Authors: Evgeniy Yu. Panov
Author institution: Department of Mathematical Analysis, Novgorod State University, B. St.-Peterburgskaya 41, 173003 Velikiy Novgorod, Russia pey@novsu.ac.ru

Summary: We propose the kinetic formulation of measure-valued and strong-measure-valued solutions of the Cauchy problem for a first-order quasilinear equation. For the corresponding kinetic equation, the class of existence and uniqueness of solutions of the Cauchy problem is constructed. This class consists of so-called entropy solutions corresponding to strong-measure-valued solutions of the original problem. In the last section, we generalize these results to the case of symmetric generally nonconservative multidimensional systems and introduce the notion of strong-measure-valued solution based solely on the kinetic approach under consideration.

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