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Global Attractors for a Nonclassical Diffusion Equation 被引量：20

Global Attractors for a Nonclassical Diffusion Equation
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摘要 We prove the existence of global attractors in H0^1 （Ω） for a nonclassical diffusion equation. Two types of nonlinearity f are considered： one is the critical exponent, and the other is the polynomial growth of arbitrary order. We prove the existence of global attractors in H0^1 （Ω） for a nonclassical diffusion equation. Two types of nonlinearity f are considered： one is the critical exponent, and the other is the polynomial growth of arbitrary order.
作者 Chun You SUN Su Yun WANG Cheng Kui ZHONG
机构地区 School of Mathematics and Statistics Department of Mathematics
出处 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2007年第7期1271-1280,共10页 数学学报（英文版）
基金 Supported in part by the NSFC,Grant(10471056) Trans-Century Training Programme Foundation for the Talents of the State Education Commission
关键词 nonclassical diffusion equation critical exponent polynomial growth of arbitrary order global attractor asymptotic a priori estimate nonclassical diffusion equation, critical exponent, polynomial growth of arbitrary order, global attractor, asymptotic a priori estimate
分类号 O175 [理学—基础数学]
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参考文献12

  • 1Aifantis, E. C.: On the problem of diffusion in solids. Acta Mech., 37, 265-296 (1980).
  • 2Lions, J. L., Magenes, E.: Non-homogeneous boundary value problems and appliations, Spring-Verlag, Berlin, 1972.
  • 3Peter, J. G., Gurtin, M. E.: On the theory of heat condition involving two temperatures. Z. Ange. Math. Phys., 19, 614-627 (1968).
  • 4Zhong, C. K., Yang, M. H., Sun, C. Y.: The existence of global attractors for the norm-to-weak continuous semigroup and its application to the nonlinear reaction-diffusion equations. J. Differential Equations, 223, 367-399 (2006).
  • 5Babin, A. V., Vishik, M. I.: Attractors of evolution equations, North-Holland, Amsterdam, 1992.
  • 6Cholewa, J. W., Dlotko, T.: Bi-spaces global attractors in abstract parabolic equations. Evol. Equations, Banach Center Publications, 60, 13-26 (2003).
  • 7Ma, Q. F., Wang, S. H., Zhong, C. K.: Necessary and sufficient conditions for the existence of global attractors for semigroups and applications. J. Indiana University Math., 51(6), (2002).
  • 8Xiao, Y. L.: Attractors for a nonclassical diffusion equation. Actc Mathematicae Applicatae Sinca, English Series, 18(1), 273-276 (2002).
  • 9Cholewa, J. W., Dlotko, T.: Global attractors in abstract parabolic problems, Cambridge University Press, Cambridge, 2000.
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同被引文献37

  • 1马巧珍,钟承奎.非经典反应扩散方程强解的全局吸引子(英文)[J].兰州大学学报（自然科学版）,2004,40(5):7-9. 被引量：5
  • 2ZHONGCHENGKUI SUNCHUNYOU NIUMINGFEI.ON THE EXISTENCE OF GLOBAL ATTRACTOR FOR A CLASS OF INFINITE DIMENSIONAL DISSIPATIVE NONLINEAR DYNAMICAL SYSTEMS[J].Chinese Annals of Mathematics,Series B,2005,26(3):393-400. 被引量：10
  • 3Aifantis E C. On the problem of diffusion in solids[J].Acta Mechanica,1980.265-296.
  • 4Lions J L,Magenes E. Non-homogeneous boundary value problems and applications[M].Berlin:springer-verlag,1972.
  • 5Kalantarov V K. On the attractors for some non-linear problems of mathematical physics[J].Zap Nauch Sem LOMI,1986.50-54.
  • 6Xiao Y L. Attractors for a nonclassical diffusion equation[J].Acta Mathematicae Applicatae Sinica,2002.273-276.
  • 7Sun C Y,Wang S Y,Zhong C K. Global attractors for a nonclassical diffusion equation[J].Acta Mathematica Scientia(English Edition),2007.1271-1280.
  • 8Wang S Y,Li D S,Zhong C K. On the dynamics of a class of nonclassical parabolic equations[J].Journal of Mathematical Analysis and Applications,2006.565-582.
  • 9Sun C,Yang M. Dynamics of the nonclassical diffusion equations[J].Asymptotic Analysis,2008,(1/2):51-81.
  • 10Eden A,Foias C,Nicolaenko B. Exponential Attractors for Dissipative Evolution Equations[M].New York:Masson Paris:Wiely,1994.

引证文献20

二级引证文献26

Acta Mathematica Sinica,English Series
2007年 第7期

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