留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

双调和型抛物方程的Schauder估计

姚锋平 周蜀林

姚锋平, 周蜀林. 双调和型抛物方程的Schauder估计[J]. 应用数学和力学, 2007, 28(11): 1340-1352.
引用本文: 姚锋平, 周蜀林. 双调和型抛物方程的Schauder估计[J]. 应用数学和力学, 2007, 28(11): 1340-1352.
YAO Feng-ping, ZHOU Shu-lin. Schauder Estimates for the Parabolic Equation of the Bi-Harmonic Type[J]. Applied Mathematics and Mechanics, 2007, 28(11): 1340-1352.
Citation: YAO Feng-ping, ZHOU Shu-lin. Schauder Estimates for the Parabolic Equation of the Bi-Harmonic Type[J]. Applied Mathematics and Mechanics, 2007, 28(11): 1340-1352.

双调和型抛物方程的Schauder估计

基金项目: 国家科技部973计划资助项目(2006CB705700);国家自然科学基金资助项目(60532080);国家教育部科学技术重点项目(306017)
详细信息
    作者简介:

    姚锋平(1978- ),江苏吴江人,博士(联系人.E-mail:yfp1123@math.pku.edu.cn);周蜀林(1966- ),贵州惠水人,博士(E-mail:szhou@math.pku.edu.cn).

  • 中图分类号: O175.26

Schauder Estimates for the Parabolic Equation of the Bi-Harmonic Type

  • 摘要: 该文给出了双调和型抛物方程初值问题解的Schauder估计,并且在适当的空间中证明了解的存在性与惟一性.类似于二阶情形,首先通过Fourier变换得到一个形式解,然后再利用位势理论和逼近方法得到解的正则性、唯一性及存在性.该方法简单而易懂.
  • [1] Schauder J.ber lineare elliptische Differentialgleichungen zweiter Ordnung[J].Math Z,1934,38(1):257-282. doi: 10.1007/BF01170635
    [2] Schauder J.Numerische Abschdtzungen in elliptischen linearen Differentialgleichungen[J].Studia Math,1934,5(1):34-42.
    [3] Campanato S.Propriet di una famiglia di spazi funzionali[J].Ann Scuola Norm Sup Pisa,1964,18(3):137-160.
    [4] Trudinger N S.A new approach to the Schauder estimates for linear elliptic equations[J].Proc Centre Math Anal Austral Nat Univ,1986,14:52-59.
    [5] Caffarelli L A.Interior a priori estimates for solutions of fully nonlinear equations[J].Ann Math,1989,130(1):189-213. doi: 10.2307/1971480
    [6] Ciliberto C.Formule di maggiorazione e teoremi di esistenza per le soluzioni delle equazioni paraboliche in due variabili[J].Ricerche Mat,1954,3(1):40-75.
    [7] Campanato S.Equazioni paraboliche del secondo ordine e spazi L[KG*2]. 2,λ(Ω;δ)[J].Ann Math Pura Appl,1966,73(4):55-102.
    [8] Simon L.Schauder estimates by scaling[J].Calc Var PDE,1997,5(5):391-407. doi: 10.1007/s005260050072
    [9] WANG Li-he.On the regularity theory of fully nonlinear parabolic equations Ⅱ[J].Comm Pure Appl Math,1992,45(2):141-178. doi: 10.1002/cpa.3160450202
    [10] Friedman A.Partial Differential Equations of Parabolic Type[M].Englewood Cliffs,NJ:Prentice-Hall Inc,1964.
    [11] Ladyzenskaja O A,Solonnikov V A,Uralceva N N.Linear and Quasilinear Equations of Parabolic Type[M].Providence, RI:American Mathematical Society,1968.
    [12] Lorenzi L.Schauder estimates for degenerate elliptic and parabolic problems with unbounded coefficients in RN[J].Differential Internat Equations,2005,18(5):531-566.
    [13] Lunardi A.Schauder theorems for linear elliptic and parabolic problems with unbounded coefficients in RN[J].Studia Math,1998,128(2):171-198.
    [14] Lunardi A.Schauder estimates for a class of degenerateelliptic and parabolic operators with unbounded coefficients in RN[J].Annali della Scuola Normale Superiore Pisa,1997,24(4):133-164.
    [15] 腾振寰.抛物型方程一般边界问题解的先验估计[J].数学进展,1965,4(3):334-386.
    [16] 王柔怀.关于一般抛物型边值问题的Schauder估计[J].吉林大学自然科学学报,1964,2(1):35-64.
    [17] Solonnikov V A.On boundary value problems for linear parabolic systems of differential equations of general form[J].Trudy Mat Inst Steklov,1965,83:3-163.
    [18] Cahn J W,Hilliard J E.Free energy of nonuniform system I. Interfacial free energy[J].J Chem Phys,1958,28(2):258-367. doi: 10.1063/1.1744102
    [19] Alikakos N D,Fusco G.Slow dynamics for the Cahn-Hilliard equation in higher space dimensions: the motion of bubbles[J].Arch Rat Mech Anal,1998,141(1):1-61. doi: 10.1007/s002050050072
    [20] Rossi R.On two classes of generalized viscous Cahn-Hilliard equations[J].Comm Pure Appl Anal,2005,4(2):405-430. doi: 10.3934/cpaa.2005.4.405
    [21] Kwembe T A.Existence and uniqueness of global solutions for the parabolic equation of the bi-harmonic type[J].Nonlinear Anal,2001,47(2):1321-1332. doi: 10.1016/S0362-546X(01)00268-1
    [22] XU Meng,ZHOU Shu-lin.Existence and uniqueness of weak solutions for a generalized thin film equation[J].Nonlinear Anal,2005,60(4):755-774. doi: 10.1016/j.na.2004.01.013
    [23] YIN Jing-xue,LIU Chang-chun.Regularity of solutions of the Cahn-Hilliard equation with concentration dependent mobility[J].Nonlinear Anal,2001,45(5):543-554. doi: 10.1016/S0362-546X(99)00406-X
    [24] DiBenedetto E.Partial Differential Equations[M].Boston-Basel-Berlin:Birkhuser,1995.
    [25] CHEN Ya-zhe,WU Lan-cheng.Second Order Elliptic Partial Differential Equations and Elliptic Systems[M].Providence,RI:American Mathematical Society,1998.
  • 加载中
计量
  • 文章访问数:  3143
  • HTML全文浏览量:  208
  • PDF下载量:  916
  • 被引次数: 0
出版历程
  • 收稿日期:  2006-10-23
  • 修回日期:  2007-08-20
  • 刊出日期:  2007-11-15

目录

    /

    返回文章
    返回