## Control and Boundary AnalysisJohn Cagnol, Jean-Paul Zolesio This volume comprises selected papers from the 21st Conference on System Modeling and Optimization in Sophia Antipolis, France. It covers over three decades of studies involving partial differential systems and equations. Topics include: the modeling of continuous mechanics involving fixed boundary, control theory, shape optimization and moving bou |

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**Initial**Value Problems Generalities Let us consider the following autonomous**initial**value problem : dy + A ( x ) = 0 on ( 0 , T ) ( with 0 < T≤ + ∞ ) , ( 0 ) with J 2 ( by non - trivial we mean. = 40. ( IVP ) dt Operator A maps a ... Page 3

... Scheme ( 2 ) is semi - constructive in the sense that we still have to solve the sub -

... Scheme ( 2 ) is semi - constructive in the sense that we still have to solve the sub -

**initial**value problem in ( 2 ) for each j . Suppose that we discretize this sub - problem using just one. Operator - Splitting Methods and Applications ... Page 4

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**initial**value problems in ( 5 ) , ( 6 ) , and ( 7 ) by schemes which are themselves second order accurate ( at least ) ; examples of such schemes can be found in , e.g. , ref . [ 10 ] ( Chapter 6 ) ( which contains also a discussion of ... Page 5

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**initial**value problem ( flow in the dynamical system terminology ) : du dt + Au + Is ( u ) = 0 on ( 0 , + ∞ ) , ( 11 ) u ( 0 ) = U0 . If we apply the Marchuk - Yanenko scheme ( 3 ) to the solution of problem ( 11 ) we obtain and for n ...Page 40

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### Contents

1 | |

DYNAMICAL SHAPE SENSITIVITY | 29 |

OPTIMAL CONTROL OF A STRUCTURAL ACOUSTIC MODEL WITH FLEXIBLE CURVED WALLS | 37 |

NONLINEAR WAVE EQUATIONS WITH DEGENERATE DAMPING AND SOURCE TERMS | 53 |

NUMERICAL MODELING OF PHASE CHANGE PROBLEMS | 63 |

SHAPE OPTIMIZATION OF FREE AIRPOROUS MEDIA TRANSMISSION COEFFICIENT | 73 |

THE UNIFORM FAT SEGMENT AND CUSP PROPERTIES IN SHAPE OPTIMIZATION | 85 |

TOPOLOGY OPTIMIZATION FOR UNILATERAL PROBLEMS | 97 |

EVOLUTION HEMIVARIATIONAL INEQUALITY WITH HYSTERESIS AND OPTIMAL CONTROL PROBLEM | 157 |

ON THE MODELING AND CONTROL OF DELAMINATION PROCESSES | 169 |

ON A SPECTRAL VARIATIONAL PROBLEM ARISING IN THE STUDY OF EARTHQUAKES | 189 |

NODAL CONTROL OF CONSERVATION LAWS ON NETWORKS | 201 |

INVARIANCE OF CLOSED SETS UNDER STOCHASTIC CONTROL SYSTEMS | 217 |

UNIFORM STABILIZATION OF AN ANISOTROPIC SYSTEM OF THERMOELASTICITY | 231 |

SEMIGROUP WELLPOSEDNESS OF A MULTILAYER MEADMARKUS PLATE WITH SHEAR DAMPING | 243 |

SOLUTION OF ALGEBRAIC RICCATI EQUATIONS ARISING IN CONTROL OF PARTIAL DIFFERENTIAL EQUATIONS | 257 |

SECOND ORDER LAGRANGE MULTIPLIER APPROXIMATION FOR CONSTRAINED SHAPE OPTIMIZATION PROBLEMS | 107 |

MATHEMATICAL MODELS OF ACTIVE OBSTACLES IN ACOUSTIC SCATTERING | 119 |

LOCAL NULL CONTROLLABILITY IN A STATE CONSTRAINED THERMOELASTIC CONTACT PROBLEM | 131 |

ON SENSITIVITY OF OPTIMAL SOLUTIONS TO CONTROL PROBLEMS FOR HYPERBOLIC HEMIVARIATIONAL INEQUALITIES | 145 |

STABILIZATION IN COMPUTING SADDLE POINTS | 281 |

SECOND ORDER SUFFICIENT CONDITIONS FOR OPTIMAL CONTROL SUBJECT TO FIRST ORDER STATE CONSTRAINTS | 293 |

Index | 305 |

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### Common terms and phrases

acoustic adjoint Algebras algorithm Anal Analysis anisotropic Applications approximation assume Banach space boundary conditions boundary value problem bounded computation consider constraints convergence convex cost functional damping defined delamination denote derivative domain dxdt eigenvalues elastic energy Eo(w exists finite formulation ghost obstacle global hemivariational inequalities hyperbolic initial iterations L²(N Lagrange multiplier Lagrangian Lasiecka Lemma linear Lipschitz Lyapunov Lyapunov equation Math Mathematics matrix method Newton-Kleinman node conditions nonlinear null controllability numerical operator operator-splitting optimal control optimal control problem optimality conditions parameters Partial Differential Equations perturbation proof Riccati equation saddle point satisfies second order Section semigroup sequence shape optimization shell shell model SIAM solution solve ßkl stochastic test problem Theorem Theory thermoelastic topology variable variational inequality vector wave equation Zolésio

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