Stochastic Nonlinear Parabolic Equations with Stratonovich Gradient Noise

Viorel Barbu; Luciano Tubaro; Zdzislaw Brzezniak

doi:10.1007/s00245-017-9409-1

Stochastic Nonlinear Parabolic Equations with Stratonovich Gradient Noise

Viorel Barbu, Luciano Tubaro^*, Zdzislaw Brzezniak

^*Corresponding author for this work

Mathematics

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	361–377
Number of pages	17
Journal	Applied Mathematics and Optimization
Volume	78
Issue number	2
Early online date	27 Mar 2017
DOIs	https://doi.org/10.1007/s00245-017-9409-1
Publication status	Published - Oct 2018

Bibliographical note

Keywords

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

Access to Document

10.1007/s00245-017-9409-1

BaBrTu_rev_14_03_2017
© Springer Science+Business Media New York 2017
Accepted author manuscript, 43.1 KB

Cite this

@article{c2796087930c4c5e97befd157dace332,

title = "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.",

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

author = "Viorel Barbu and Luciano Tubaro and Zdzislaw Brzezniak",

note = "{\textcopyright} Springer Science+Business Media New York 2017",

year = "2018",

month = oct,

doi = "10.1007/s00245-017-9409-1",

language = "English",

volume = "78",

pages = "361–377",

journal = "Applied Mathematics and Optimization",

issn = "0095-4616",

publisher = "Springer",

number = "2",

}

TY - JOUR

T1 - Stochastic Nonlinear Parabolic Equations with Stratonovich Gradient Noise

AU - Barbu, Viorel

AU - Tubaro, Luciano

AU - Brzezniak, Zdzislaw

N1 - © Springer Science+Business Media New York 2017

PY - 2018/10

Y1 - 2018/10

N2 - 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.

AB - 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.

KW - Multiplicative gradient-type Stratonovich noise

KW - Nonlinear singular-degenerate stochastic partial differential equation

KW - Stochastic optimal control

KW - Stochastic variational inequalities

UR - http://www.scopus.com/inward/record.url?scp=85016107611&partnerID=8YFLogxK

U2 - 10.1007/s00245-017-9409-1

DO - 10.1007/s00245-017-9409-1

M3 - Article

AN - SCOPUS:85016107611

SN - 0095-4616

VL - 78

SP - 361

EP - 377

JO - Applied Mathematics and Optimization

JF - Applied Mathematics and Optimization

IS - 2

ER -

Stochastic Nonlinear Parabolic Equations with Stratonovich Gradient Noise

Abstract

Bibliographical note

Keywords

Access to Document

Other files and links

Cite this