Discrete and Continuous Dynamical Systems - S
January 2022 , Volume 15 , Issue 1
Issue on partial differential equations, optimization and their applications
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This work deals with a geometric inverse source problem. It consists in recovering inclusion in a fixed domain based on boundary measurements. The inverse problem is solved via a shape optimization formulation. Two cost functions are investigated, namely, the least squares fitting, and the Kohn-Vogelius function. In this case, the existence of the shape derivative is given via the first order material derivative of the state problems. Furthermore, using the adjoint approach, the shape gradient of both cost functions is characterized. Then, the stability is investigated by proving the compactness of the Hessian at the critical shape for both considered cases. Finally, based on the gradient method, a steepest descent algorithm is developed, and some numerical experiments for non-parametric shapes are discussed.
In the present work we introduce and study a new method for solving the inverse obstacle problem. It consists in identifying a perfectly conducting inclusion
This paper deals with Sylvester and Stein tensor equations with low rank right hand sides. It proposes extended Krylov-like methods for solving Sylvester and Stein tensor equations. The expressions of residual norms are presented. To show the performance of the proposed approaches, some numerical experiments are given.
Data completion known as Cauchy problem is one most investigated inverse problems. In this work we consider a Cauchy problem associated with Helmholtz equation. Our concerned is the convergence of the well-known alternating iterative method [
In this case, we present theoretical results of the convergence of this relaxed algorithm. Meanwhile it, we can deduce the convergence intervals related to the relaxation parameters in different situations. In contrast to the existing results, the proposed algorithm is simple to implement converges for all choice of wave number.
We approach our algorithm using finite element method to obtain an accurate numerical results, to affirm theoretical results and to prove it's effectiveness.
We consider a weakly damped cubic nonlinear Schrödinger equation with Dirac interaction defect in a half line of
This paper describes the state of the art and gives a survey of the wide literature published in the last years on the fractional Laplacian. We will first recall some definitions of this operator in
The aim of this paper is to prove existence and regularity of solutions for the following nonlinear singular parabolic problem
By extending some linear time delay systems stability techniques, this paper, focuses on continuous time delay nonlinear systems (TDNS) dependent delay stability conditions. First, by using the Takagi Sugeno Fuzzy Modeling, a novel relaxed dependent delay stability conditions involving uncommon free matrices, are addressed in Linear Matrix Inequalities (LMI). Then, as application a Nonlinear Carbon Dioxide Model is used and rewritten by a change of coordinate to the interior equilibrium point. Next, by using the non-linearity sector method the model is transformed to a corresponding Fuzzy Takagi Sugeno (TS) multi-model. Also, the maximum delay margin to which the model is stable, is identified. Finally, to prove the analytic results a numerical simulation is also performed and compared to other methods.
We study a simplified multidimensional version of the phenomenological surface growth continuum model derived in [
We establish some results regarding the existence of solutions to a nonlinear mono-energetic singular transport equation in slab geometry on
A methodology for fault-tolerant-control(FTC) is proposed that compensates actuator failures in active suspension systems (ASS). This methodology is based on a Frequency Domain approach that represents failures using a scale factor to optimize the ASS and improve ride comfort. The controller design is carried out using off-the-shelf tools based on linear matrix inequalities (LMIs), guaranteeing asymptotic stability, compensating the effect of actuator faults, and ensuring certain
In this paper, we establish the existence of weak solution in Orlicz-Sobolev space for the following Kirchhoff type probelm
In this paper, we study the existence of positive solutions of the following equation
The study of the problem
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