AAM  >> Vol. 3 No. 1 (February 2014)

    一类非线性发展方程整体强解的存在性研究
    The Existence of Global Strong Solution for a Class of Nonlinear Evolution Equations

  • 全文下载: PDF(297KB)    PP.1-7   DOI: 10.12677/AAM.2014.31001  
  • 下载量: 1,758  浏览量: 5,795   科研立项经费支持

作者:  

李妍汝,李青松,马加磊:长沙理工大学数学与计算科学学院,长沙

关键词:
非线性发展方程方程Galerkin方法整体强解多项式指数增长Nonlinear Evolution Equations; Galerkin Method; Global Strong Solution; Polynomial Exponential Growth

摘要:

本文主要研究一类非线性发展方程整体强解的适定性问题,我们利用Galerkin方法和能量估计方法得到初边值问题整体强解的存在唯一性,以及对初值的连续依赖性。所得的结果是最新的,其中非线性项满足任意多项式指数增长条件。

The well-posed problem of global strong solution for a class of nonlinear evolution equations is studied in this paper. By applying the method of Galerkin and energy estimate, we obtain the existence and uniqueness of global strong solution of the following initial boundary value problem, and the continuous dependence of initial data. The result of the paper is the latest, where the nonlinear term f satisfies arbitrary polynomial exponential growth condition.

文章引用:
李妍汝, 李青松, 马加磊. 一类非线性发展方程整体强解的存在性研究[J]. 应用数学进展, 2014, 3(1): 1-7. http://dx.doi.org/10.12677/AAM.2014.31001

参考文献

[1] Aifantis, E.C. (1980) On the problem of diffusion in solids. Acta Mechanica, 37, 265-296.
[2] Xiao, Y.L. (2002) Attractors for a nonclassical diffusion equation. Acta Mathematicae Applicatae Sinica (English Series), 18, 273-276.
[3] Sun, C.Y., Wang, S.Y. and Zhong, C.K. (2007) Global attractors for a non¬classical diffusion equation. Acta Mathematica Sinica (English Series), 23, 1271-1280.
[4] Robinson, J.C. (2001) Infinite-dynamical systems. Cambr¬idge University Press, Cambridge, 285-303.
[5] Wang, S.Y., Li, D.S. and Zhong, C.K. (2006) On the dynamics of a class of nonclassical parabolic equations. Journal of Mathematical Analysis and Applications, 317, 565-582.
[6] Jiang, Y. and Xie, Y.Q. (2010) Global attractors for a class nonlinear evolu¬tion equation. Mathematical Theory and Applications, 30, 24-28.
[7] Xie, Y.Q. and Deng, J.B. (2010) Global attractors for a class of nonlinear evolution equations. Mathematical Theory and Application¬s, 30, 13- 19.