Open AccessDIRICHLET PROBLEM FOR LOADED DEGENERATING EQUATION OF THE MIXED TYPE IN THE RECTANGULAR AREA
Author(s) -
Екатерина Петровна Мелишева
Publication year - 2013
Publication title -
vestnik samarskogo universiteta. estestvennonaučnaâ seriâ
Language(s) - English
Resource type - Journals
eISSN - 2712-8954
pISSN - 2541-7525
DOI - 10.18287/2541-7525-2013-19-6-40-53
Subject(s) - uniqueness , eigenfunction , mathematics , mathematical analysis , domain (mathematical analysis) , dirichlet problem , boundary value problem , type (biology) , work (physics) , dirichlet boundary condition , series (stratigraphy) , stability (learning theory) , dirichlet distribution , boundary (topology) , eigenvalues and eigenvectors , physics , computer science , paleontology , ecology , quantum mechanics , machine learning , biology , thermodynamics
In this work necessary and sufficient conditions for uniqueness of a solution to the first boundary problem for Lavrentiev-Bitsadze equation in rectangular domain are established. The solution to the problem is constructed as a sum of series with respect of eigenfunctions of a corresponding one-dimensional Stour-m-Liouviele problem. The stability is shown.