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The Self-similar Solution to Some Nonlinear Integro-differential Equations Corresponding to Fractional Order Time Derivative
作者姓名:Chang  Xing  MIAO  Han  YANG
作者单位:[1]Institute of Applied Physics and Computational Mathematics, P. O. Box 8009, Beijing 100088, P. R. China [2]Department of Mathematics, Southwest Jiaotong University, Chengdu 610031, P. R. China
基金项目:The first author is supported by NSF of China, Special Funds for Major State Basic Research Projects of China and NSF of Chinese Academy of Engineering Physics
摘    要:In this paper we study the self-similar solution to a class of nonlinear integro-differential equations which correspond to fractional order time derivative and interpolate nonlinear heat and wave equation. Using the space-time estimates which were established by Hirata and Miao in 1] we prove the global existence of self-similar solution of Cauchy problem for the nonlinear integro-differential equation in C*(0,∞];B^8pp,∞(R^n).

关 键 词:自相似解  空间时间估计  Integro微分方程  时间导数  Mittag-Lettter函数  柯西问题
收稿时间:2003-08-20
修稿时间:2003-08-20

The Self–similar Solution to Some Nonlinear Integro–differential Equations Corresponding to Fractional Order Time Derivative
Chang Xing MIAO Han YANG.The Self-similar Solution to Some Nonlinear Integro-differential Equations Corresponding to Fractional Order Time Derivative[J].Acta Mathematica Sinica,2005,21(6):1337-1350.
Authors:Chang Xing Miao  Han Yang
Institution:(1) Institute of Applied Physics and Computational Mathematics, 8009, Beijing 100088, P. R. China;(2) Department of Mathematics, Southwest Jiaotong University, Chengdu 610031, P. R. China
Abstract:In this paper we study the self–similar solution to a class of nonlinear integro–differential equations which correspond to fractional order time derivative and interpolate nonlinear heat and wave equation. Using the space–time estimates which were established by Hirata and Miao in 11] we prove the global existence of self–similar solution of Cauchy problem for the nonlinear integro-differential equation in $$
C_{*} (0,\infty );\dot{B}^{{s_{p} }}_{{p,\infty }} (\mathbb{R}^{n} )).
$$ The first author is supported by NSF of China, Special Funds for Major State Basic Research Projects of China and NSF of Chinese Academy of Engineering Physics
Keywords:Self–  similar solution  Space–  time estimates  Integro-differential equation  Fractional order          time derivative  Mittag–  Leffler’  s function  Cauchy problem
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