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PARABOLIC EXPLOSIVE SYSTEMS
Uniqueness Results for 4th Order Operators with Irregular
42 other sections not shown
admissible pairs analogous assume assumption Banach space boundary conditions boundary control bounded in L*(q bounded set Cauchy problem Chapter closed convex set compact support control-state cost function deduce defined denoted Dirichlet Dirichlet condition dxdt eacists a triplet Existence of Optimal f in Q fact finite follows given going to prove hence Hilbert spaces infj introduce J. L. LIONS Lemma linear Lº Q Lºco lºo LT Q Method of Approach minimizing sequence non-empty closed convex obtain open set optimal control optimal pair u,y priori estimates problem Proof of Theorem reductio ad absurdum regular Remark resp result satisfies scalar product Section set of admissible set of L*(q Singular Optimality System space strong L*(q Subsection Theorem Theorem 2.1 unique solution weak solution weak star whence y-za z-za