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

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.

Document Details

Document Type
Technical Report
Publication Date
Jan 31, 1969
Accession Number
AD0694390

Entities

People

  • V. P. Lavrenchuk

Organizations

  • National Air and Space Intelligence Center

Tags

DTIC Thesaurus Topics

  • Boundaries
  • Boundary Value Problems
  • Coefficients

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis