## Control of Distributed Singular Systems |

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### Contents

PARABOLIC EXPLOSIVE SYSTEMS | 1 |

UNSTABLE SYSTEMS AND WITH MISSING DATA | 15 |

EMBEDDING AND UNIQUENESS | 20 |

Copyright | |

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analogous arbitrary assume assumption Banach space boundary conditions BOUNDARY CONTROL bounded set Cauchy problem Chapter choose closed convex set consider the equation consider the system cost function deduce defined Dirichlet Dirichlet condition dxdt example exist optimal pairs existence of optimal exists a triplet f in Q fact finite follows given going to prove Green's formula hence infJ infJ(v.z introduce J.L. LIONS Lemma Let us consider LZ(Q MAGENES Method of Approach minimizing sequence Multiplying non-empty closed convex notation obtain open set optimal control optimal pair u,y parabolic priori estimates Proof of Theorem reductio ad absurdum regular relatively compact set Remark resp satisfies scalar product Section set of admissible Singular Optimality System space strong L Q Theorem 2.2 triplet u,y,p unique solution uniqueness theorem unstable system weak L Q weak solution weak star y-zd yields