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具变指数非线性拟抛物方程弱解的存在性 被引量：2

The Existence of Weak Solutions for a Nonlinear Pseudoparabolic Equation with Variable Exponent
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摘要 虑一类变指数的非线性拟抛物方程的初值问题.在一些初值的假定下,基于时间离散化方法构造逼近解.通过对逼近解的一致性估计,证明了弱解的存在性. We consider an initial-boundary value problem for a class of nonlinear pseu- doparabolic equation involving variable exponent. Under some assumptions on the initial value, we construct approximate solutions by using the time-discrete method. By means of uniform estimates on these approximate solutions, we establish the existence of weak solutions.
作者 郭金勇
机构地区 柳州师范高等专科学校数学与计算机科学系
出处 《数学的实践与认识》 CSCD 北大核心 2012年第12期222-229,共8页 Mathematics in Practice and Theory
关键词 变指数 非线性拟抛物方程 弱解 存在性 variable exponent nonlinear pseudoparabolic equation weak solution existence
分类号 O175.26 [理学—基础数学]
  • 相关文献

参考文献11

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  • 4Fan X, Zhang Q. Existence of solutions for p(x)-Laplacian Dirichlet problem[J]. Nonlinear Analysis, TMA, 2003, 52: 1843-1852.
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  • 7郭金勇.一个粘性非线性源的p-Laplace发展方程弱解的存在性[J].钦州学院学报,2006,21(6):10-13. 被引量：7
  • 8郭金勇.一个粘性非线性源的p-Laplace发展方程弱解的唯一性[J].柳州师专学报,2007,22(2):112-114. 被引量：5
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二级参考文献27

  • 1郭金勇.一个粘性非线性源的p-Laplace发展方程弱解的存在性[J].钦州学院学报,2006,21(6):10-13. 被引量：7
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共引文献6

同被引文献15

  • 1郭金勇.一个粘性非线性源的p-Laplace发展方程弱解的存在性[J].钦州学院学报,2006,21(6):10-13. 被引量：7
  • 2郭金勇.一个粘性非线性源的p-Laplace发展方程弱解的唯一性[J].柳州师专学报,2007,22(2):112-114. 被引量：5
  • 3CaoY, Yin J X, Jin C H. A periodic problem of a semilinear pseudoparabolic equation [ J ]. Hindawi Pub- lishing Corporation Abstract and Applied Analysis, 2011 : Art 363579, 27pp.
  • 4Guo B L. Initial boundary value problem for one class of system of multidimensional inhomogeneous GBBM equa- tions [ J ]. Chinese Annals of Mathematics, 1987,8 B ( 2 ) : 226 - 239.
  • 5Fax X, Zhao D. The quasi-minimizer of integral function- als with m (x) growth conditions [ J ]. Nonlinear Analy- sis : Theory, Methods & Applications, 2000, 39 (7) : 807 -816.
  • 6Kovacik O, ROkosnik J. On spaces Lp(x) and Wk,p(x) [J].Czechoslovak Mathematical Journal, 1991,41 (4) : 592 - 618.
  • 7Guo B L. Initial boundary value problem for one class of system of multidimensional inhomogeneous GBBM equations[J].{H}Chinese Annals of Mathematics,1987,(02):226-239.
  • 8Kaikina E I. Initial-boundary value problem for nonlinear pseudoparabolic equations in a critical case[J].Electronic JDE,2007.1-25.
  • 9Kovú ík O,Rkosník J. On spaces Lp(x) and Wk,p(x)[J].{H}Czechoslovak Math J,1991.592-618.
  • 10Fan X,Zhang Q. Existence of solutions for p,(x)-Laplacian Dirichlet problem[J].{H}Nonlinear Analysis TMA,2003.1843-1852.

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数学的实践与认识
2012年 第12期

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