This article is cited in 9 papers

Locally Bounded Generalized Entropy Solutions to the Cauchy Problem for a First-Order Quasilinear Equation

A. Yu. Goritskii^a, E. Yu. Panov<sup>b

a</sup> M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
^b Novgorod State University after Yaroslav the Wise

Abstract: Generalized entropy solutions for a first-order quasilinear partial differential equation are studied. It is shown that the Cauchy problem for this equation is ill-posed in the class of locally bounded functions. The examples of nonexistence and nonuniqueness of solutions are constructed. Moreover, a uniqueness theorem, which holds for solutions integrable with respect to the spatial variable, is proved.

UDC: 517.95

Received in December 2000

 English version: Proceedings of the Steklov Institute of Mathematics, 2002, 236, 110–123

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