ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

10. Partial Differential Equations

1991 MS Classification: 35 Panov Evgeniy Yu., Novgorod University, Russia On some hyperbolic systems of conservation laws. We study Cauchy problem for the nonstrictly hyperbolic system U_{t} + f(U)_{x} = 0, U = U(t, x) lies in a space of real symmetric or complex Hermitian 2 × 2-matrixes; t ≥ 0, x ∈ R; f(U) is a function of a matrix U defined by some scalar function f ∈ C(R). We introduce a notion of a strong generalized entropy solution; prove that it exists, is unique, satisfies all Kruzhkov-Lax entropy conditions and for general enough case can be obtained by a vanishing viscosity method. Reference: E. Yu. Panov, A class of systems of quasilinear conservation laws, Matematicheskii Sbornik. 188:5 (1997), 725-751.