The self-similar solution to some nonlinear integro-differential equations corresponding to fractional order time derivative

被引：5
|
作者：
Miao, CX
Yang, H
机构：
[1] Inst Appl Phys & Computat Math, Beijing 100088, Peoples R China
[2] SW Jiaotong Univ, Dept Math, Chengdu 610031, Peoples R China
来源：
ACTA MATHEMATICA SINICA-ENGLISH SERIES | 2005年 / 21卷 / 06期
基金：
美国国家科学基金会; 中国国家自然科学基金;
关键词：
self-similar solution; space-time estimates; integro-differential equation; fractional order time derivative; Mittag-Leffler's function; Cauchy problem;
D O I：
10.1007/s10114-005-0546-0
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
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 [11] we prove the global existence of self-similar solution of Cauchy problem for the nonlinear integro-differential equation in C-* ([0, infinity); B-p,infinity(sp) (R-n)).
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页码：1337 / 1350
页数：14
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