An analytic solution for a non-local initial-boundary value problem including a partial differential equation with variable coefficients

Document Type : Research Paper


1 Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran.

2 Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran


‎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.


Main Subjects

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