Global Well-posedness of the Stochastic Generalized Kuramoto-Sivashinsky Equation with Multiplicative Noise

被引：0

作者：

Wei WU ^{[1
,2
]}

Shang-bin CUI ^{[2
]}

Jin-qiao DUAN ^{[3
,4
]}

机构：

[1] Science and Information College, Qingdao Agricultural University

[2] Department of Mathematics, Sun Yat-Sen University

[3] Department of Applied Mathematics, Illinois Institute of Technology

[4] Center for Mathematical Sciences, Huazhong University of Science and Technology

来源：

ActaMathematicaeApplicataeSinica | 2018年 / 34卷 / 03期

基金：

美国国家科学基金会; 中国国家自然科学基金;

关键词：

Kuramoto-Sivashinsky equation; stochastic partial differential equations; multiplicative noise; well-posedness;

D O I：

暂无

中图分类号：

O175 [微分方程、积分方程];

学科分类号：

070104 ;

摘要：

Global well-posedness of the initial-boundary value problem for the stochastic generalized KuramotoSivashinsky equation in a bounded domain D with a multiplicative noise is studied. It is shown that under suitable sufficient conditions, for any initial data u0 ∈L;（D×?）, this problem has a unique global solution u in the space L;(?, C([0, T ], L;（D）)) for any T > 0, and the solution map u0 →u is Lipschitz continuous.

引用

页码：566 / 584

页数：19

共 10 条

[1] NONLINEAR STOCHASTIC WAVE EQUATIONS: BLOW-UP OF SECOND MOMENTS IN L 2-NORM [J] . Pao-Liu Chow.&nbsp&nbspThe Annals of Applied Probability . 2009 (6)
[2] Dynamics for the stochastic nonlocal Kuramoto–Sivashinsky equation [J] . Desheng Yang.&nbsp&nbspJournal of Mathematical Analysis and Applications . 2006 (1)
[3] Global L2-solutions of stochastic Navier-Stokes equations
Mikulevicius, R
Rozovskii, BL
[J]. ANNALS OF PROBABILITY, 2005, 33 (01) : 137 - 176
[4] A note on stochastic Burgers' system of equations
Twardowska, K
Zabczyk, J
[J]. STOCHASTIC ANALYSIS AND APPLICATIONS, 2004, 22 (06) : 1641 - 1670
[5] On the stochastic Kuramoto–Sivashinsky equation [J] . Jinqiao Duan,Vincent J. Ervin.&nbsp&nbspNonlinear Analysis . 2001 (2)
[6] On the existence of a solution to stochastic Navier–Stokes equations [J] . Marek Capiński,Szymon Peszat.&nbsp&nbspNonlinear Analysis . 2001 (2)
[7] A Stochastic Nonlinear Schr?dinger Equation?with Multiplicative Noise [J] . A. de Bouard,A. Debussche.&nbsp&nbspCommunications in Mathematical Physics . 1999 (1)
[8] Existence and uniqueness results for semilinear stochastic partial differential equations
Gyongy, I
[J]. STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 1998, 73 (02) : 271 - 299
[9] On the Korteweg-de Vries-Kuramoto-Sivashinsky equation [J] . H. A. Biagioni,J. L. Bona,R. J. Iório,M. Scialom.&nbsp&nbspAdvances in Differential Equations . 1996 (1)
[10] Instability and turbulence of wavefronts in reaction-diffusion systems .2 Yoshiki Kuramoto. Prog. Theor. Phys . 1980

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