I. V. Kolos, M. V. Kolos, “Solvability of the generalized Dirichlet problem for hyperbolic equations”, Num. Meth. Prog., 2002, Volume 3, Issue 1,Pages <nobr>161

Solvability of the generalized Dirichlet problem for hyperbolic equations

I. V. Kolos^a, M. V. Kolos^b

^a University of Russian Education Academy, Moscow
^b Lomonosov Moscow State University, Research Computing Center

Abstract: A priory inequalities with a negative norm are obtained for hyperbolic differential equations with Dirichlet boundary conditions for the case when the right-hand sides belong to a space of generalized functions. The existence and uniqueness of a generalized solution to the problem as well as the convergence of an approximate method are proved.

Keywords: generalized Dirichlet problem, hyperbolic equations, numerical methods, generalized functions.

UDC: 519.6