%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