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Sufficient conditions for optimality for differential inclusions of parabolic type and duality. (English) Zbl 1149.49027

Summary: Sufficient conditions for optimality are derived for partial differential inclusions of parabolic type on the basis of the apparatus of locally conjugate mapping, and duality theorems are proved. The duality theorems proved allow one to conclude that a sufficient condition for an extremum is an extremal relation for the direct and dual problems.

MSC:

49K20 Optimality conditions for problems involving partial differential equations
35R70 PDEs with multivalued right-hand sides
35K99 Parabolic equations and parabolic systems
49K24 Optimal control problems with differential inclusions (nec./ suff.) (MSC2000)
54C60 Set-valued maps in general topology
49N15 Duality theory (optimization)
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