‎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 ...

In this paper, we give the spectral theory for eigenvalues and eigenfunctions of a boundary value problem consisting of the linear fractional Bessel operator. Moreover, we show that this operator is self-adjoint, the eigenvalues of the problem are real, and the corresponding eigenfunctions are orthogonal. In this paper, we give the spectral theory for eigenvalues and eigenfunctions...

FOLLOING OUR PREVIOS PROJECT [1], WE ARE GOING TO PROVE THE EXISTENCE AND UNIQUENESS OF THE SOLUTION OF THE SPECTRAL PROBLEM IN THIS PROJECT.FIRST,WE HAVE PROVEN THE UNIQUENESS OF THE SOLUTION THEN TO PROVE THE EXISTRNCE WE CONSTENSS OF THE ADJOINT PROBLEM CORRESPONDING TO THIS SPECTRAL PROBLEM NEXT THE UNIQUESS OF THE ADJOINT PROBLEM IS THE EXISTENCE OF THE MAIN PROBLEM AS DISCUSSED BY[2] AND ...

‎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 ...

‎in this paper‎, ‎we find matrix representation of a class of sixth order sturm-liouville problem (slp) with separated‎, ‎self-adjoint boundary conditions and we show that such slp have finite spectrum‎. ‎also for a given matrix eigenvalue problem $hx=lambda vx$‎, ‎where $h$ is a block tridiagonal matrix and $v$ is a block diagonal matrix‎, ‎we find a sixth order boundary value problem of atkin...

in this paper, the conjugate gradient method coupled with adjoint problem is used in order to solve the inverse heat conduction problem and estimation of the time- dependent heat flux using the temperature distribution at a point in a three layer system with none homogeneous boundary conditions. also, the effect of noisy data on final solution is studied. for solving this problem the general co...

in this manuscript, we study the inverse problem for non self-adjoint sturm--liouville operator $-d^2+q$ with eigenparameter dependent boundary and discontinuity conditions inside a finite closed interval. by defining  a new hilbert space and  using its spectral data of a kind, it is shown that the potential function can be uniquely determined by part of a set of values of eigenfunctions at som...

In this paper has been studied the wave equation in some non-classic cases. In the  rst case boundary conditions are non-local and non-periodic. At that case the associated spectral problem is a self-adjoint problem and consequently the eigenvalues are real. But the second case the associated spectral problem is non-self-adjoint and consequently the eigenvalues are complex numbers,in which two ...

The main purpose of this study is to estimate the step heat fluxes applied to the wall of a two-dimensional symmetric channel with turbulent flow. For inverse analysis, conjugate gradient method with adjoint problem is used. In order to calculate the flow field,   two equation model is used. In this study, adjoint problem is developed to conduct an inverse analysis of heat transfer in a channel...

‎in this paper‎, ‎we study spectral element approximation for a constrained‎ ‎optimal control problem in one dimension‎. ‎the equivalent a posteriori error estimators are derived for‎ ‎the control‎, ‎the state and the adjoint state approximation‎. ‎such estimators can be used to‎ ‎construct adaptive spectral elements for the control problems.