This article is cited in 1 paper

MATHEMATICAL MODELING AND NUMERICAL SIMULATION

Correctness of task family with nonclassical boundary conditions

A. Yu. Mokin

Moscow State University, Faculty of Computational Mathematics and Cebernetics, MSU, Uchebniy Korpus 2, GSP-1, Leninskiye Gory, Moscow, 119991, Russia

Abstract: A boundary value problem for partial differential equation with nonlocal boundary relations of special type is resolved by means of a slight modification of the separation of variables method. Ordinal differential operator of the second order subject to boundary conditions of the main problem is not self-adjoint. The system of eigenfunctions generated by the operator has no basis property in $L_2[0,1]$ space. A special system of functions is proposed to expand the solution of the boundary value problem.

Keywords: boundary conditions, parabolic type problem, separation of variables method.

Received: 24.03.2008

DOI: 10.20537/2076-7633-2009-1-2-139-146