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15

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## Publications

Publications (15)

We analyze the sidewise controllability for the variable coefficients one-dimensional wave equation. The control is acting on one extreme of the string with the aim that the solution tracks a given path or profile at the other free end. This sidewise profile control problem is also often referred to as nodal profile or tracking control. The problem...

In this paper, we study a three step iterative scheme to estimate fixed points of non-expansive mappings in the framework of Banach spaces. Further, some convergence results are proved for such mappings. A nontrivial numerical example is presented to verify our assertions and main results. Finally, we approximate the solution of a boundary value pr...

In this paper, by using variational approach, Mountain Pass Theorem and Krasnoselskii’s genus theory, we show the existence and multiplicity of solutions for a Schrödinger–Kirchhoff type equation involving the fractional \(p\left( .,.\right)\)-Laplacian in fractional Sobolev space with variable exponent. We also establish a Bartsch–Wang type compac...

In this study, we have reported experiments on interlayer performance of single and multi walled carbon nanotubes (SWCNTs and MWCNTs) for fabrication of n-InP substrates based diode applications and characterized with various methods to obtain ideal parameters. Structural and morphological properties of the nanotubes have been investigated by X-ray...

This study aims to investigate the problem of determining the unknown initial temperature in a variable coefficient heat equation. We obtain the existence and uniqueness of the solution of the optimal control problem considered under some conditions. Using the adjoint problem approach, we get the Frechet differential of the cost functional. We cons...

This paper studies the minimization problem governed by a wave equation with homogeneous Neumann boundary condition and where the control function is a initial velocity of the system. We give necessary conditions for the existence and uniqueness of the optimal solution. We get the Frechet derivation of the cost functional via the solution of the co...

In this paper, we consider the weak solutions of hyperbolic problems subject to inhomogeneous Dirichlet and Neumann boundary conditions. Using Fourier–Galerkin method, we obtain approximate solutions of the problems and test the obtained results on numerical examples by MAPLE®.

We get symbolic and numeric solutions developing a MAPLE (R) program which uses the initial velocity on the state variable of a wave equation as control function. Solution of this problem implies the minimization at the final time of the distance measured in a suitable norm between the solution of the problem and a given target. An iterative algori...

We use the initial condition on the state variable of a hyperbolic problem as control function and formulate a control problem whose solution implies the minimization at the final time of the distance measured in a suitable norm between the solution of the problem and given targets. We prove the existence and the uniqueness of the optimal solution...

We theoretically study the problem of controlling the initial velocity from a given final state in a wave equation. Getting the Frechet differential of the cost functional and Lipschitz continuity of the gradient, we constitute a minimizer for the cost functional and obtain its convergence rate.

We investigate the problem of controlling the boundary functions in a one dimensional hyperbolic problem by minimizing the functional including the final state. After proving the existence and uniqueness of the solution to the given optimal control problem, we get the Frechet differential of the functional and give the necessary condition to the op...

In this paper, we apply the Galerkin method to the problem of vibration of a one-dimensional system with free end conditions. Giving a MAPLE®procedure, we test the results on two numerical examples.

We control the function f(x) in the problem J α (f)=y(x 1 ;f)-b] 2 +α∥f∥ L 2 [x 0 ,x 1 ] 2 →min subject to y ' +p(x)=f(x); y(x 0 )=a. We propose an efficient MAPLE procedure for obtaining the optimal control.