This article is cited in 2 papers

Proceedings of conferences

On well-posedness of a mixed problem for the wave equation

V. M. Gordienko<sup>ab

a</sup> Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia
^b Novosibirsk State University

Abstract: We consider a mixed problem in a quarter-space for the wave equation with two spatial variables. The boundary condition is a linear combination of the first derivatives.
We study boundary conditions under which the mixed problem satisfies the Lopatinskii condition. The established criterion is constructive. Namely, we verify that a second order polynomial is Hurwitzian. Coefficients of the polynomial are defined explicitly by the coefficients of the boundary condition of the mixed problem.
We prove well-posedness of the problems satisfying the Lopatinskii condition by means of constructing a dissipative energy integral allowing us to obtain easily a priori estimate. To construct the dissipative energy integral we solve a system of linear algebraic equations.

Keywords: wave equation, mixed problem, dissipative energy integral.

UDC: 517.956.32

MSC: 13A99

Received March 5, 2010