Accession Number : AD0694390

Title :   GENERAL BOUNDARY-VALUE PROBLEMS FOR PARABOLIC SYSTEMS WITH INCREASING COEFFICIENTS,

Corporate Author : FOREIGN TECHNOLOGY DIV WRIGHT-PATTERSON AFB OHIO

Personal Author(s) : Lavrenchuk,V. P.

Report Date : 31 JAN 1969

Pagination or Media Count : 9

Abstract : The solution of a general boundary-value problem for Petrovsky parabolic systems with increasing coefficients is analyzed. For such a boundary value problem the Green matrix is constructed and its upper bound is established. The general form of the boundary value problem solution is written in terms of the Green matrix and the problem of the permissible growth of the system coefficients, which ensure the existence of solutions in the same class of functions as for the boundary value problems for systems with bounded coefficients, is analyzed. In the case of a Dirichlet problem for second order systems with sufficiently smooth coefficients, the problem of extending the class of functions established above, in which solutions of the boundary-value problem exist, is analyzed under the assumption that the system is dissipative in the sense of Petrovsky.

Descriptors :   (*PARTIAL DIFFERENTIAL EQUATIONS, *BOUNDARY VALUE PROBLEMS), MATRICES(MATHEMATICS), INEQUALITIES, THEOREMS, USSR

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE