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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Applied mathematics & optimization 30 (1994), S. 113-126 
    ISSN: 1432-0606
    Keywords: Nonconvex variational problems ; Relaxation ; Optimal control ; 49J27 ; 35B25 ; 65N30
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract An optimal control problem for a multivalued system governed by a nonconvex variational problem, involving a regularization parameter ɛ〉0, is proposed and studied. The solution to the variational problem exhibits typically rapid oscillations (a so-called fine structure) corresponding to a multiphase state of the material. We want to control only this fine structure. Existence of an optimal control is proved. Its convergence with ɛ→0 is studied by means of an optimal control problem for a relaxed variational problem involving (suitably generalized) Young measures. The uniqueness of the solution to the relaxed variational problem, which is nontrivial but is very important in the context of optimal control, is studied in special cases. A finite-element approximation is proposed.
    Type of Medium: Electronic Resource
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