QUALITATIVE PROPERTIES OF SOLUTIONS TO A TIME-SPACE FRACTIONAL EVOLUTION EQUATION

被引：59
|
作者：
Fino, Ahmad Z. [1 ]
Kirane, Mokhtar [2 ]
机构：
[1] Lebanese Univ, LaMA Liban, Tripoli, Lebanon
[2] Univ La Rochelle, Dept Math, F-17042 La Rochelle, France
来源：
QUARTERLY OF APPLIED MATHEMATICS | 2012年 / 70卷 / 01期
关键词：
Parabolic equation; fractional Laplacian; Riemann-Liouville fractional integrals and derivatives; local existence; critical exponent; blow-up rate; BLOW-UP; CAUCHY-PROBLEM; DIFFUSION;
D O I：
10.1090/S0033-569X-2011-01246-9
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this article, we analyze a. spatio-temporally nonlocal nonlinear parabolic equation. First, we validate the equation by an existence-uniqueness result. Then, we show that blowing-up solutions exist and study their time blow-up profile. Also, a result on the existence of global solutions is presented. Furthermore, we establish necessary conditions for local or global existence.
引用
收藏
页码：133 / 157
页数：25
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