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A relation between Г-convergence of functionals and their associated gradient flows 被引量:3

A relation between Γ-convergence of functionals and their associated gradient flows
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摘要 Giorgi conjectured in 1979 that if a sequence of functionals converges in the sense of P-convergence to a limiting functional, then the corresponding gradient flows will converge as well after changing timescale appropriately. It is shown that this conjecture holds true for a rather wide kind of functionals. Giorgi conjectured in 1979 that if a sequence of functionals converges in the sense of P-convergence to a limiting functional, then the corresponding gradient flows will converge as well after changing timescale appropriately. It is shown that this conjecture holds true for a rather wide kind of functionals.
作者 简怀玉
出处 《Science China Mathematics》 SCIE 1999年第2期133-139,共7页 中国科学:数学(英文版)
基金 Project supported by the National Natural Science Foundation of China (Grant No. 19701018)
关键词 Γ-convergence PARABOLIC EQUATIONS PARABOLIC MINIMA ASYMPTOTIC behaviour. Γ-convergence, parabolic equations, parabolic minima, asymptotic behaviour.
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参考文献3

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同被引文献24

  • 1范辉军.Existence of the self-similar solutions in the heat flow of harmonic maps[J].Science China Mathematics,1999,42(2):113-132. 被引量:3
  • 2简怀玉.HOMOGENIZATION PROBLEMS OF PARABOLIC MINIMA[J].Acta Mathematicae Applicatae Sinica,1996,12(3):318-327. 被引量:1
  • 3简怀玉.一类拟线性抛物方程的均匀化[J].应用数学学报,1996,19(4):549-558. 被引量:3
  • 4Huaiyu Jian.A relation between Г-convergence of functionals and their associated gradient flows[J]. Science in China Series A: Mathematics . 1999 (2)
  • 5Chen Ya-Zhe,E. DiBenedetto.H?lder estimates of solutions of singular parabolic equations with measurable coefficients[J]. Archive for Rational Mechanics and Analysis . 1992 (3)
  • 6N. Fusco,G. Moscariello.On the homogenization of quasilinear divergence structure operators[J]. Annali di Matematica Pura ed Applicata . 1986 (1)
  • 7Hans Wilhelm Alt,Stephan Luckhaus.Quasilinear elliptic-parabolic differential equations[J]. Mathematische Zeitschrift . 1983 (3)
  • 8Huijun Fan.Existence of the self-similar solutions in the heat flow of harmonic maps[J].Science in China Series A: Mathematics.1999(2)
  • 9Huaiyu Jian.A relation between Г-convergence of functionals and their associated gradient flows[J].Science in China Series A: Mathematics.1999(2)
  • 10Nelly André,Itai Shafrir.Asymptotic Behavior of Minimizers for the Ginzburg-Landau Functional with Weight. Part I[J].Archive for Rational Mechanics and Analysis.1998(1)

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