[1]李卓,李霞.时间周期哈密尔顿系统的Ergodic行为[J].南京师范大学学报(自然科学版),2020,43(01):18-22.[doi:10.3969/j.issn.1001-4616.2020.01.004]
　LiZhuo,LiXia.ErgodicBehavioroftheTimePeriodicHamiltonSystem[J].JournalofNanjingNormalUniversity(NaturalScienceEdition),2020,43(01):18-22.[doi:10.3969/j.issn.1001-4616.2020.01.004]
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时间周期哈密尔顿系统的Ergodic行为()
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《南京师范大学学报》（自然科学版）[ISSN:1001-4616/CN:32-1239/N]

卷:
第43卷
期数:
2020年01期
页码:
18-22
栏目:
·数学·
出版日期:
2020-03-15

文章信息/Info

Title:
ErgodicBehavioroftheTimePeriodicHamiltonSystem
文章编号:
1001-4616(2020)01-0018-05
作者:
李卓; 李霞
苏州科技大学数理学院,江苏苏州215009
Author(s):
LiZhuo; LiXia
SchoolofMathematicsandPhysics,SuzhouUniversityofScienceandTechnology,Suzhou215009,China
关键词:
Hamilton-Jacobi方程; 粘性解; 临界值
Keywords:
Hamilton-Jacobiequation; viscositysolution; criticalvalue
分类号:
O193
DOI:
10.3969/j.issn.1001-4616.2020.01.004
文献标志码:
A
摘要:
本文拟用PDE方法,在时间1-周期Hamilton函数H(x,t,p)关于(x,t,p)连续,关于p强制条件下,证明存在(-overc)≤(～overc)∈R,使得函数u(x,t)-(～overc)t在Tn×[0,∞)有下界,u(x,t)-(～overc)t在Tn×[0,∞)有上界,其中u(x,t)是Hamilton-Jacobi方程的粘性解.
Abstract:
thispaper,weintendtousethePDEmethodtoprovethatthereexists(-overc)≤(～overc)∈Rsuchthatu(x,t)-(-overc)tisboundedfrombelowandu(x,t)-(～overc)tisboundedfromaboveonTn×[0,∞)whenthetime1-periodicHamiltonianfunctionH(x,t,p)iscontinuouson(x,t,p)andcoerciveonp,whereu(x,t)istheviscositysolutionoftheassociatedHamilton-Jacobiequation.

参考文献/References:

[1]ISHIIH.AshortintroductiontoviscositysolutionsandthelargetimebehaviourofsolutionsofH-Jequations[C]//Hamilton-Jacobiequations:approximation,numbericalanalysisandapplications.Cetraro,Italy:Springer,2013:111-249.
[2]MATHERJ.ActionminimizinginvariantmeasuresforpositivedefiniteLagrangiansystems[J].Mathematischezeitschrift,1991,207:169-207.
[3]AL-AIDAROUSES,ALZAHRANIEO,ISHIIH,etal.AconvergenceresultfortheergodicproblemforHamilton-JacobiequationswithNeumann-typeboundaryconditions[J].ProceedingsoftheRoyalsocietyofEdinburghsectionamathematics,2016,146:225-242.
[4]DAVINIA,FATHIA,ITURRIAGAR,etal.Convergenceofthesolutionsofthediscountedequations:thediscretecase[J].Mathematischezeitschrift,2016,284:1021-1034.
[5]DAVINIA,FATHIA,ITURRIAGAR,etal.ConvergenceofthesolutionsofthediscountedHamilton-Jacobiequation:convergenceofthediscountedsolutions[J].Inventionsmathematicae,2016,206:29-55.
[6]GOMESDA,MITAKEH,TRANHV.TheselectionproblemfordiscountedHamilton-Jacobiequations:somenon-convexcases[J/OL].ArXive-prints,2016.
[7]ISHIIH,MITAKEH,TRANHV.ThevanishingdiscountproblemandviscosityMathermeasures.Part1:theproblemonatorus[J/OL].Arxive-prints,2016.
[8]MITAKEH,TRANHV.SelectionproblemsforadiscountdegenerateviscousHamiltonJacobiequation[J].Advancesinmathematics,2017,306:684-703.
[9]LIX.Long-timeasymptoticsolutionsofconvexHamilton-Jacobiequationsdependingonunknownfunctions[J].Discreteandcontinuousdynamicalsystems,2017,37:5151-5562.

备注/Memo

备注/Memo:
收稿日期:2018-10-16.
基金项目:国家自然科学基金面上项目(11471238)、苏州科技大学研究生科研创新计划项目(SKYCX_16011).
通讯作者:李霞,博士,副教授,研究方向:哈密尔顿动力系统.E-mail:lixia0527@188.com
更新日期/Last Update: 2020-03-15