ON INITIAL VALUE AND TERMINAL VALUE PROBLEMS FOR SUBDIFFUSIVE STOCHASTIC RAYLEIGH-STOKES EQUATION

被引：14

作者：

Caraballo, Tomas ^{[1
]}

Tran Bao Ngoc ^{[2
]}

Tran Ngoc Thach ^{[3
]}

Nguyen Huy Tuan ^{[4
,5
]}

机构：

[1] Univ Seville, Fac Matemat, Dept Ecuac Diferenciales & Anal Numer, C Tarfia S-N, Seville 41012, Spain

[2] Duy Tan Univ, Inst Res & Dev, Da Nang 550000, Vietnam

[3] Ton Duc Thang Univ, Fac Math & Stat, Appl Anal Res Grp, Ho Chi Minh City, Vietnam

[4] Univ Sci, Dept Math & Comp Sci, Ho Chi Minh City, Vietnam

[5] Vietnam Natl Univ, Ho Chi Minh City, Vietnam

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B | 2021年 / 26卷 / 08期

关键词：

Time-fractional Rayleigh-Stokes equation; Wiener process; existence and regularity properties of solution; REACTION-DIFFUSION EQUATIONS; GENERALIZED 2ND-GRADE FLUID; EVOLUTION EQUATIONS; DERIVATIVE DRIVEN; DYNAMICS; SUBJECT; REGULARITY; SPACE;

D O I：

10.3934/dcdsb.2020289

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we study two stochastic problems for time-fractional Rayleigh-Stokes equation including the initial value problem and the terminal value problem. Here, two problems are perturbed by Wiener process, the fractional derivative are taken in the sense of Riemann-Liouville, the source function and the time-spatial noise are nonlinear and satisfy the globally Lipschitz conditions. We attempt to give some existence results and regularity properties for the mild solution of each problem.

引用

页码：4299 / 4323

页数：25

共 36 条

[1]

[Anonymous], 1992, STOCHASTIC EQUATIONS

[2] An analysis of the Rayleigh-Stokes problem for a generalized second-grade fluid [J].

Bazhlekova, Emilia ;

Jin, Bangti ;

Lazarov, Raytcho ;

Zhou, Zhi .

NUMERISCHE MATHEMATIK, 2015, 131 (01) :1-31

[3] Well-Posedness of the Multidimensional Fractional Stochastic Navier-Stokes Equations on the Torus and on Bounded Domains [J].

Debbi, Latifa .

JOURNAL OF MATHEMATICAL FLUID MECHANICS, 2016, 18 (01) :25-69

[4] A computational study of the one-dimensional parabolic equation subject to nonclassical boundary specifications [J].

Dehghan, M .

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, 2006, 22 (01) :220-257

[5] A finite element method for the numerical solution of Rayleigh-Stokes problem for a heated generalized second grade fluid with fractional derivatives [J].

Dehghan, Mehdi ;

Abbaszadeh, Mostafa .

ENGINEERING WITH COMPUTERS, 2017, 33 (03) :587-605

[6] The one-dimensional heat equation subject to a boundary integral specification [J].

Dehghan, Mehdi .

CHAOS SOLITONS & FRACTALS, 2007, 32 (02) :661-675

[7] The Rayleigh-Stokes problem for an edge in a generalized Oldroyd-B fluid [J].

Fetecau, Corina ;

Jamil, Muhammad ;

Fetecau, Constantin ;

Vieru, Dumitru .

ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, 2009, 60 (05) :921-933

[8] Regularity of the solution for a final value problem for the Rayleigh-Stokes equation [J].

Hoang Luc Nguyen ;

Huy Tuan Nguyen ;

Zhou, Yong .

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2019, 42 (10) :3481-3495

[9] Identifying initial condition of the Rayleigh-Stokes problem with random noise [J].

Hoang Luc Nguyen ;

Huy Tuan Nguyen ;

Mokhtar, Kirane ;

Xuan Thanh Duong Dang .

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2019, 42 (05) :1561-1571

[10] Dynamic output feedback covariance control of stochastic dissipative partial differential equations [J].

Hu, Gangshi ;

Lou, Yiming ;

Christofides, Panagiotis D. .

CHEMICAL ENGINEERING SCIENCE, 2008, 63 (18) :4531-4542

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