Open AccessNONLOCAL PROBLEM WITH INTEGRAL CONDITION FOR A FOURTH ORDER EQUATION
Author(s) -
Наталья Викторовна Бейлина
Publication year - 2014
Publication title -
vestnik samarskogo universiteta. estestvennonaučnaâ seriâ
Language(s) - English
Resource type - Journals
eISSN - 2712-8954
pISSN - 2541-7525
DOI - 10.18287/2541-7525-2014-20-10-26-37
Subject(s) - subsequence , mathematics , uniqueness , sobolev space , limit (mathematics) , sequence (biology) , space (punctuation) , a priori and a posteriori , convergence (economics) , scheme (mathematics) , galerkin method , integral equation , limit of a sequence , variable (mathematics) , order (exchange) , mathematical analysis , computer science , finite element method , finance , economics , philosophy , genetics , thermodynamics , physics , epistemology , bounded function , biology , economic growth , operating system
In this paper, we consider a nonlocal problem with integral condition with respect to spacial variable for a forth order partial dierential equation. The conditions on the data for unique solvability of the problem in Sobolev space are determined. Proving of uniqueness of generalized solution is based on acquired apriori estimates. To prove the solvability we use a following scheme: sequence of approximate solutions using Galerkin procedure is built, apriory estimates that allow to extract from it a convergent subsequence are received, on the nal stage it is shown that the limit of subsequence is the required generalized solution.