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PARABOLIC EXPLOSIVE SYSTEMS
UNSTABLE SYSTEMS AND WITH MISSING DATA
EMBEDDING AND UNIQUENESS
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analogous arbitrary assume assumption Banach space boundary conditions BOUNDARY CONTROL bounded set Chapter closed convex set consider the cost consider the equation control-state cost function deduce defined denoted Dirichlet Dirichlet condition dxdt example exist optimal pairs existence of optimal exists a triplet fact finite follows given going to prove Green's formula hence infJ infJ(v,z introduce J.L. LIONS Lemma Let us consider linear LZ(Q Method of Approach minimizing sequence Multiplying non-empty closed convex obtain open set optimal control optimal pair u,y priori estimates Proof of Theorem reductio ad absurdum regular Remark resp satisfies scalar product Section set of admissible Singular Optimality System space strong L Q Theorem 2.1 triplet u,y,p unique solution uniqueness theorem unstable system v e Uad weak sense weak solution weak star y-zd yields z e L Q z e L6(Q