%0 Journal Article
%T An analytic solution for a non-local initial-boundary value problem including a partial differential equation with variable coefficients
%J Bulletin of the Iranian Mathematical Society
%I Iranian Mathematical Society (IMS)
%Z 1017-060X
%A Jahanshahi, M.
%A Darabadi, M.
%D 2016
%\ 04/01/2016
%V 42
%N 2
%P 315-326
%! An analytic solution for a non-local initial-boundary value problem including a partial differential equation with variable coefficients
%K Partial Differential Equation
%K Boundary Value Problem
%K Self Adjoint Problem
%K Non-Self Adjoint Operators
%K Non-Local-Boundary Conditions
%R
%X This paper considers a non-local initial-boundary value problem containing a first order partial differential equation with variable coefficients. At first, the non-self-adjoint spectral problem is derived. Then its adjoint problem is calculated. After that, for the adjoint problem the associated eigenvalues and the subsequent eigenfunctions are determined. Finally the convergence of series solution and the uniqueness of this solution will be proved.
%U http://bims.iranjournals.ir/article_761_706ebf130c6496e7db6e47caf0549442.pdf