[1]何 兴,陈光淦*.有界区间上的随机非局部Ginzburg-Landau方程[J].四川师范大学学报(自然科学版),2018,(04):450-455.[doi:10.3969/j.issn.1001-8395.2018.04.0040450-04.004]
 HE Xing,CHEN Guanggan.Stochastic Nonlocal Ginzburg-Landau Equation on Bounded Intervals[J].Journal of SichuanNormal University,2018,(04):450-455.[doi:10.3969/j.issn.1001-8395.2018.04.0040450-04.004]
点击复制

有界区间上的随机非局部Ginzburg-Landau方程()
分享到:

《四川师范大学学报(自然科学版)》[ISSN:1001-8395/CN:51-1295/N]

卷:
期数:
2018年04期
页码:
450-455
栏目:
基础理论
出版日期:
2018-04-15

文章信息/Info

Title:
Stochastic Nonlocal Ginzburg-Landau Equation on Bounded Intervals
文章编号:
1001-8395(2018)04-0450-06
作者:
何 兴1 陈光淦2*
1.四川大学 锦江学院, 四川 彭山 620860;
2.四川师范大学 数学与软件科学学院, 四川 成都 610066
Author(s):
HE Xing1 CHEN Guanggan2
1.College of Jinjiang, Sichuan University, Pengshan 620860, Sichuan;
2.College of Mathematics and Software Science, Sichuan Normal University, Chengdu 610066, Sichuan
关键词:
研究有界区间上随机非局部Ginzburg-Landau方程.通过在适当的加权空间上考虑克服有界区间上非局部Laplace算子带来的困难运用一系列精致估计获得系统的某些有界性利用胎紧解决噪声给系统带来的通常意义下的紧性问题最终利用Skorokhod定理以及鞅表示定理获得系统鞅解的存在性.
Keywords:
stochastic Ginzburg-Landau equation bounded intervals nonlocal laplacian operator martingale solution
分类号:
O175.2
DOI:
10.3969/j.issn.1001-8395.2018.04.0040450-04.004
文献标志码:
A
摘要:
研究有界区间上随机非局部Ginzburg-Landau方程.通过在适当的加权空间上考虑,克服有界区间上非局部Laplace算子带来的困难,运用一系列精致估计获得系统的某些有界性,利用胎紧解决噪声给系统带来的通常意义下的紧性问题,最终利用Skorokhod定理以及鞅表示定理获得系统鞅解的存在性.
Abstract:
This paper deals with the stochastic nonlocal Ginzburg-Landau equation on bounded intervals.By introducing a weighted sobolev space, it overcomes the difficulties caused by the nonlocal Laplacian operator on bounded domains.By using a series of precise estimate, the boundedness of the system is established.By using the tightness to solve the general compact problem caused by noise, it finally obtains the existence of martingale solutions for the system by Skorokhod embedding theorem and representation theorem.

参考文献/References:

[1] ZASLAVSKY G M.Chaos, fractional kinetics, and anomalous transport[J].Physics Reports,2002,371(6):461-580.
[2] NIGMATULLIN R R.The realization of the generalized transfer equation in a medium with fractal geometry[J].Physica Status Solidi,1986,133(1):425-430.
[3] 汤小松,罗节英.一类分数阶p-Laplace方程积分三点边值问题正解的存在性[J].四川师范大学学报(自然科学版),2014,37(6):867-874.
[4] GUO B L, HUO Z.Global well-posedness for the fractional nonlinear Schrödinger equation[J].Communication in Partial Differential Equations,2010,36(2):247-255.
[5] GUO B L, ZENG M.Solution for the fractional Landau-Lifshitz equation[J].J Math Anal Appl,2010,361(1):131-138.
[6] PU X K, GUO B L.Global weak solution of the fractional Landau-Lifshitz-Maxwell equation[J].J Math Anal Appl,2010,372(1):86-98.
[7] VASILY E T, GEORGE M Z.Fractional Ginzburg-Landau equation for fractal media[J].Physica,2005,A354(1):249-261.
[8] LU H, LÜ S J.Random attracor for fractional Ginzburg-Landau equantion with multiplicative noise[J].Taiwanese J Mathematics,2014,18(2):435-450.
[9] DU Q, GUNZBURGER M, LEHOUCQ R B, et al.Analysis and approximation of nonlocal diffusion problems with volume constraints[J].SIAM Rev,2012,54(4):667-696.
[10] CHEN Z Q, MEERSCHAERT M M, NANE E.Space-time fractional diffusion on bounded domains[J].J Math Anal Appl,2012,393(2):479-488.
[11] NEZZA E D, PALATUCCI G, VALDINOCI E.Hitchhiker's guide to the fractional Sobolev spaces[J].Bull Sci Math,2011,136(5):521-573.
[12] DU Q, GUNZBURGER M, LEHOUCQ R B, et al.A nonlocal vector calculus, nonlocal volume-constrained problems, and nonlocal balance laws[J].Mathematical Models & Methods in Applied Sciences,2013,23(3):493-540.
[13] FLANDOLI F, GATAREK D.Maitingale and stationary solutions for stochastic Navier-Stokes equations[J].Probability Theory & Related Fields,1995,102(3):367-391.
[14] DA PRATO G, ZABCZYK J.Stochastic Equations in Infinite Dimensions[M].Cambridge:Cambridge University Press,1992.
[15] BRZEZNIAK Z, MOTYL E.Existence of a martingale solution of the stochastic Navier-Stokes equations in unbounded 2D and 3D and 3mains[J].J Differential Equations,2013,254(4):1627-1685.

备注/Memo

备注/Memo:
收稿日期:2016-06-07 接受日期:2017-09-11
基金项目:国家自然科学基金(11571245和11401409)和四川省教育厅重点科研项目(15ZA0031)
*通信作者简介: 陈光淦(1978—),男,教授,主要从事随机偏微分方程的研究,E-mail:chenqingjan@sicnu.edu.cn
更新日期/Last Update: 2018-04-15