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一个动态边值问题解的存在性讨论 被引量：3

Existence of Solutions to a Dynamic Boundary Value Problem
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摘要 讨论源于流体动力学的一类抛物型方程非局部动态边值问题.结合Sobolev-Slobodeckij空间和不动点定理证明解的存在唯一性. A dynamic boundary value problem of parabolic equation is investigated. Existence of classic solutions is proved by combining the Sobolev-Slobodeckij space theory and fixed point theorem.
作者 王远弟 石本磊
机构地区 上海大学理学院
出处 《上海大学学报（自然科学版）》 CAS CSCD 北大核心 2012年第5期496-499,共4页 Journal of Shanghai University:Natural Science Edition
基金 上海市教委重点学科建设资助项目(J50101)
关键词 抛物型方程 非局部 边值问题 parabolic equation nonlocal boundary value problem
分类号 O175.2 [理学—基础数学]
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参考文献11

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共引文献6

同被引文献21

  • 1叶其孝 李正元.反应扩散方程引论[M].北京：科学出版社,1999..
  • 2CRISCIANI F, PURINI a. A note on the dynamic boundary conditions in Munklike circulation models [J]. The European Physical Journal B, 2003, 31: 571-575.
  • 3KUNDU P K, COHEN I M. Fluid mechanics [M]. San Diego: Academic Press, 2008.
  • 4ROLL H U. Physics of the marine atmosphere [M]. San Diego: Academic Press, 1965.
  • 5WU H, ZHENG S. Convergence to equilibrium for the Cahn-Hilliard equation with dynamic boundary conditions [J]. J Differential Equations, 2004, 204(2): 511-531.
  • 6NICA O, PRECUP R. On the nonlocal initial value problem for first order differential systems [J]. Stud Univ Babe~-Bolyai Math, 2011, 56(3): 113-125.
  • 7BYSZEWSKI L. Theorems about the existence and uniqueness of solutions of a semilinear evolu- tion nonlocal Cauchy problem [J]. J of Math Anal and Appl, 1991, 162(2): 494-505.
  • 8BABAK P. Nonlocal initial problems for coupled reaction-diffusion systems and their applica- tions [J]. Nonlinear Analysis: Real World Applications, 2007, 8(3): 980-996.
  • 9PUL'KINA L S. A nonlocal problem with integral conditions for a hyperbolic equation [J]. Dif- ferential Equations, 2004, 40(7): 947-953.
  • 10LI F, LIANG ~], LU T T, et al. A nonlocal Cauchy problem for fractional integro differential equations [J], J of Applied Math, 2012, DOI: 10.1155/2012/901942.

引证文献3

上海大学学报（自然科学版）
2012年 第5期

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