Stochastic Nonlinear Parabolic Equations with Stratonovich Gradient Noise

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JournalApplied Mathematics and Optimization
DateAccepted/In press - 27 Mar 2017
DateE-pub ahead of print - 27 Mar 2017
DatePublished (current) - Oct 2018
Issue number2
Volume78
Number of pages17
Pages (from-to)361–377
Early online date27/03/17
Original languageEnglish

Abstract

Existence and uniqueness of solutions to stochastic differential equation (Formula presented.) in (Formula presented.); (Formula presented.), (Formula presented.), (Formula presented.) on (Formula presented.) is studied. Here (Formula presented.) is a bounded and open domain of (Formula presented.), (Formula presented.), (Formula presented.) is a divergence free vector field, (Formula presented.) is a continuous and monotone mapping of subgradient type and (Formula presented.) are independent Brownian motions in a probability space (Formula presented.). The weak solution is defined via stochastic optimal control problem.

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© Springer Science+Business Media New York 2017

    Research areas

  • Multiplicative gradient-type Stratonovich noise, Nonlinear singular-degenerate stochastic partial differential equation, Stochastic optimal control, Stochastic variational inequalities

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