Stochastic Nonlinear Parabolic Equations with Stratonovich Gradient Noise

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.

Metadata

Authors/Creators:	Barbu, Viorel Tubaro, Luciano Brzezniak, Zdzislaw https://orcid.org/0000-0001-8731-6523
Copyright, Publisher and Additional Information:	© Springer Science+Business Media New York 2017
Keywords:	Multiplicative gradient-type Stratonovich noise, Nonlinear singular-degenerate stochastic partial differential equation, Stochastic optimal control, Stochastic variational inequalities
Dates:	Accepted: 27 March 2017 Published (online): 27 March 2017 Published: October 2018
Institution:	The University of York
Academic Units:	The University of York > Faculty of Sciences (York) > Mathematics (York)
Depositing User:	Pure (York)
Date Deposited:	14 Jun 2017 14:45
Last Modified:	30 Jan 2024 00:14
Published Version:	https://doi.org/10.1007/s00245-017-9409-1
Status:	Published
Refereed:	Yes
Identification Number:	https://doi.org/10.1007/s00245-017-9409-1
Related URLs:	http://www.scopus.com/inward/record.url?...

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Stochastic Nonlinear Parabolic Equations with Stratonovich Gradient Noise

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