In this manuscript, we consider 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. We prove by defining a new Hilbert space and using spectral data of a kind, the potential function can be uniquely determined by a set of value of eigenfunctions at an interior point and p...

New formulas on the inverse problem for the continuous skewself-adjoint Dirac type system are obtained. For the discrete skewself-adjoint Dirac type system the solution of a general type inverse spectral problem is also derived in terms of the Weyl functions. The description of the Weyl functions on the interval is given. BorgMarchenko type uniqueness theorems are derived for both discrete and ...

Spectral stability analysis for solitary waves is developed in the context of the Hamiltonian system of coupled nonlinear Schrödinger equations. The linear eigenvalue problem for a non-self-adjoint operator is studied with two self-adjoint matrix Schrödinger operators. Sharp bounds on the number and type of unstable eigenvalues in the spectral problem are found from the inertia law for quadrati...

The current work concerns the study and the implementation of a modern algorithm for error estimation in CFD computations. This estimate involves the dealing of the adjoint argument. By solving the adjoint problem, it is possible to obtain important information about the transport of the error towards the quantity of interest. The aim is to apply for the first time this procedure into Petrov-Ga...

A mathematical model is presented in the present study to control‎ ‎the light propagation in an inhomogeneous media‎. ‎The method is ‎based on the identification of the optimal materials distribution‎ ‎in the media such that the trajectories of light rays follow the‎ ‎desired path‎. ‎The problem is formulated as a distributed parameter ‎identification problem and it is solved by a numerical met...

Optimal control of fractional linear systems on a finite horizon can be classically formulated using the adjoint system. But the adjoint of a causal fractional integral or derivative operator happens to be an anti-causal operator: hence, the adjoint equations are not easy to solve in the first place. Using an equivalent diffusive realization helps transform the original problem into a coupled s...

The behavior of analytic and numerical adjoint solutions is examined for the quasi-1D Euler equations. For shocked ow, the derivation of the adjoint problem reveals that the adjoint variables are continuous with zero gradient at the shock and that an internal adjoint boundary condition is required at the shock. A Green's function approach is used to derive the analytic adjoint solutions corresp...