Optimal relaxed control of stochastic hereditary evolution equations with Lévy noise

Utpal Manna, Debopriya Mukherjee

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Existence theory of optimal relaxed control problem for a class of stochastic hereditary evolution equations driven by Lévy noise has been studied. We formulate the problem in the martingale sense of Stroock and Varadhan to establish existence of optimal controls. The construction of the solution is based on the classical Faedo-Galerkin approximation, the compactness method and the Jakubowski version of the Skorokhod theorem for nonmetric spaces, and certain compactness properties of the class of Young measures on Suslin metrizable control sets. As application of the abstract theory, Oldroyd and Jeffreys fluids have been studied and existence of optimal relaxed control is established. Existence and uniqueness of a strong solution and uniqueness in law for the two-dimensional Oldroyd and Jeffreys fluids are also shown.
Original languageEnglish
Article number61
JournalControl, optimisation and calculus of variations
Issue number48
Publication statusE-pub ahead of print - 25 Oct 2019
Externally publishedYes


  • Hereditary evolution equations
  • Jeffreys fluid
  • Martingale solution
  • Oldroyd fluid
  • Relaxed controls
  • Young measure

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