in this paper, the goursat problem of a third order equation on cases of explicit solvability isinvestigated, with the help of the riemann function. some results and one theorem are given concerning theexistence and uniqueness for the solution of the suggested problem.

as a sequel of the recent works, we would like to discuss another stage for the solution of the mixed problem which considers the concepts of well operated conditions applicable to the solution of mixed problem, i.e. the existence and uniqueness of the solution must always conformable with some assumptions.

As a sequel of the recent works, we would like to discuss another stage for the solution of the mixed problem which considers the concepts of well operated conditions applicable to the solution of mixed problem, i.e. the existence and uniqueness of the solution must always conformable with some assumptions.

‎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 ...