scholarly journals Optimal Control of a Nonlinear PDE Governed by Fractional Laplacian

2021 ◽  
Author(s):  
Rafał Kamocki
Keyword(s):  
Optimal Control ◽  
Fractional Laplacian ◽  
Nonlinear Pde ◽  
Optimal Solutions ◽  
Dirichlet Laplacian ◽  
Existence Of Optimal Solutions ◽  
Closure Theorem ◽  
Orientor Fields ◽  
Lower Closure ◽  
Lower Closure Theorem

AbstractWe consider an optimal control problem containing a control system described by a partial nonlinear differential equation with the fractional Dirichlet–Laplacian, associated to an integral cost. We investigate the existence of optimal solutions for such a problem. In our study we use Filippov’s approach combined with a lower closure theorem for orientor fields.

A lower closure theorem for autonomous orientor fields

1988 ◽  
Vol 110 (3-4) ◽  
pp. 249-254 ◽  
Author(s):  
Luigi Ambrosio
Keyword(s):  
Differential Inclusion ◽  
Closure Property ◽  
Closure Theorem ◽  
Set Valued Mapping ◽  
Orientor Fields ◽  
Lower Closure ◽  
Lower Closure Theorem ◽  
Image Position

SynopsisGiven a set valued mapping ∑: ℝ → ∑n, we prove a closure property with respect to -convergence for the differential inclusionunder very mild assumptions on ∑.

scholarly journals Optimal control of nonlinear second order evolution equations

1993 ◽  
Vol 6 (2) ◽  
pp. 123-135 ◽  
Author(s):  
N. U. Ahmed ◽  
Sebti Kerbal
Keyword(s):  
Optimal Control ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Second Order ◽  
Nonlinear Evolution Equations ◽  
Optimal Solutions ◽  
Existence Of Optimal Solutions ◽  
Lagrange Problem

In this paper we study the optimal control of systems governed by second order nonlinear evolution equations. We establish the existence of optimal solutions for Lagrange problem.

scholarly journals Continuous dependence and optimal control of a dynamic elastic-viscoplastic contact problem with non-monotone boundary conditions

2022 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Xilu Wang ◽  
Xiaoliang Cheng
Keyword(s):  
Optimal Control ◽  
Boundary Conditions ◽  
Continuous Dependence ◽  
Initial Conditions ◽  
Weak Form ◽  
Constitutive Law ◽  
Optimal Solutions ◽  
Existence Of Optimal Solutions ◽  
External Forces ◽  
Weak Topologies

<p style='text-indent:20px;'>In this paper, we consider continuous dependence and optimal control of a dynamic elastic-viscoplastic contact model with Clarke subdifferential boundary conditions. Since the constitutive law of elastic-viscoplastic materials has an implicit expression of the stress field, the weak form of the model is an evolutionary hemivariational inequality coupled with an integral equation. By providing some equivalent weak formulations, we prove the continuous dependence of the solution on external forces and initial conditions in the weak topologies. Finally, the existence of optimal solutions to a boundary optimal control problem is established.</p>

Optimal control of static contact in finite strain elasticity

2020 ◽  
Vol 26 ◽  
pp. 95
Author(s):  
Anton Schiela ◽  
Matthias Stoecklein
Keyword(s):  
Optimal Control ◽  
Finite Strain ◽  
Path Following ◽  
Contact Problems ◽  
Finite Deformations ◽  
Elastic Contact ◽  
Optimal Solutions ◽  
Existence Of Optimal Solutions ◽  
Static Contact ◽  
Convergence Of Sequences

We consider the optimal control of elastic contact problems in the regime of finite deformations. We derive a result on existence of optimal solutions and propose a regularization of the contact constraints by a penalty formulation. Subsequential convergence of sequences of solutions of the regularized problem to original solutions is studied. Based on these results, a numerical path-following scheme is constructed and its performance is tested.

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