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On kinetic formulation of first-order hyperbolic quasilinear systems

On kinetic formulation of first-order hyperbolic quasilinear systems

We give kinetic formulation of measure valued and strong measure valued solutions to the Cauchy problem for a first-order quasilinear equation. For the corresponding kinetic equation the class of existence and uniqueness to the Cauchy problem is extracted. This class consists of so-called entropy so...

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Bibliographic Details
Main Author: Panov, E.Yu.
Format: Article
Language:English
Published: Інститут прикладної математики і механіки НАН України 2004
Series:Український математичний вісник
Online Access:http://dspace.nbuv.gov.ua/handle/123456789/124631
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Summary:We give kinetic formulation of measure valued and strong measure valued solutions to the Cauchy problem for a first-order quasilinear equation. For the corresponding kinetic equation the class of existence and uniqueness to the Cauchy problem is extracted. This class consists of so-called entropy solutions, which correspond to strong measure valued solutions of the original problem. In the last section we generalized these results to the case of symmetric generally nonconservative multidimensional systems and introduce the notion of a strong measure valued solution, based only on the kinetic approach under consideration.

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