## 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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**obtained**from authentic and highly regarded sources. Reprinted material is quoted with permission, and sources are indicated. A wide variety of references are listed. Reasonable efforts have been made to publish reliable data and ... Page 4

... , in the case where J = 2, we

... , in the case where J = 2, we

**obtain**(with tn+1/2 = t” + T/2): *" = 20. (4) then, for n > 0, assuming that p" is known, we compute p" via dip - + A = n in-H1/2 dt –– 1(p, t) 0 On (t , t ), (5) *(t”) = 2*, 2*1/2 = p(t"+1/2), dip n ... Page 5

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**obtain**u0 = u0, (12) and for n ≥ 0, un being known, un+1/2 − un τ+ Aun+1/2 = 0, (13) un+1 − un+1/2τ+∂IS(un+1)=0. (14) Relation (13) implies un+1/2 = (I+τA)−1un. (15) On the other Operator-Splitting Methods and Applications 5.Page 20

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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 continuous convergence convex cost functional damping defined Definition delamination denote derivative domain dynamic eigenvalues elastic energy exists fat segment property fluid formulation Geometry given global hemivariational inequalities hyperbolic hysteresis invariant iterations Lagrange multiplier Lagrangian Lasiecka Lemma linear Lipschitz Lyapunov Lyapunov equation Math Mathematics matrix mesh method MPEC Newton-Kleinman node conditions nonlinear null controllability numerical obtain operator operator-splitting optimal control optimal control problem optimality conditions Partial Differential Equations perturbation respect Riccati equation saddle point satisfies second order Section semigroup sequence shape optimization shell shell model SIAM solve stochastic test problem Theory thermoelastic topological derivatives topology uniform cusp property uniform fat segment variable variational inequality vector velocity wave equation Zolésio

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