Mathematical life

The works of the S.K. Godunov seminar on hyperbolic equations

V. M. Gordienko<sup>ab

a</sup> Sobolev Institute of Mathematics, 4, Koptyuga ave., Novosibirsk, 630090, Russia
^b Novosibirsk State University, 2, Pirogova str., Novosibirsk, 630090, Russia

Abstract: In the middle of 1970s at Novosibirsk State University the S. K. Godunov seminar on hyperbolic equations started its work. The article describes the works of the participants on hyperbolic equations. The main interest was concentrated around two problems. The first is the reduction of a high-order Petrovskiĭ hyperbolic equation to a first-order Friedrichs hyperbolic symmetric system. The second probem is that if a boundary value problem is posed for a hyperbolic equation then it is required to reduce it to a symmetric system so that the posed boundary condition be dissipative.

Keywords: wave equation, mixed problem, symmetric hyperbolic system, dissipative boundary condition.

UDC: 517.956.32

MSC: 35L20

Received December 18, 2019, published March 25, 2020