## Analysis and Control of Nonlinear Infinite Dimensional SystemsAnalysis and Control of Nonlinear Infinite Dimensional Systems |

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### Contents

1 | |

35 | |

Chapter 3 Controlled Elliptic Variational Inequalities | 125 |

Chapter 4 Nonlinear Accretive Differential Equations | 199 |

Chapter 5 Optimal Control of Parabolic Variational Inequalities | 315 |

Chapter 6 Optimal Control in Real Time | 407 |

459 | |

475 | |

### Other editions - View all

Analysis and Control of Nonlinear Infinite Dimensional Systems Viorel Barbu No preview available - 1993 |

### Common terms and phrases

a.e. in Q a.e. t E a.e. t G a.e. x E Q accretive approximating arbitrary but ﬁxed assume assumptions Ay(t Banach space Barbu boundary value problem bounded subset Brézis C0-semigroup Cauchy problem Chapter compact completes the proof condition convex function Corollary deﬁned deﬁnition denoted differential equations duality mapping E D(A elliptic equivalently estimate exists ﬁll ﬁnite follows free boundary Hence Hilbert space implies inﬁnitesimal Lebesgue measure Lemma lim sup linear locally Lipschitz lower semicontinuous m-accretive maximum principle mild solution monotone operators Moreover multiply Eq nonlinear norm obstacle problem optimal control problem optimal pair parabolic problem 1.1 Proof Let proof of Theorem Proposition 1.1 readily seen reﬂexive satisﬁes scalar product Section semigroup solution to Eq Stefan problem strong solution subdifferential tend to zero Theorem 1.1 uniformly convex unique solution variational inequalities viscosity solution weak star weakly X X X yields