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
相关论文
共 50 条
  • [1] Qualitative properties of solutions to a nonlinear time-space fractional diffusion equation
    Borikhanov, Meiirkhan. B. B.
    Ruzhansky, Michael
    Torebek, Berikbol. T. T.
    [J]. FRACTIONAL CALCULUS AND APPLIED ANALYSIS, 2023, 26 (01) : 111 - 146
  • [2] Qualitative properties of solutions to a nonlinear time-space fractional diffusion equation
    Meiirkhan B. Borikhanov
    Michael Ruzhansky
    Berikbol T. Torebek
    [J]. Fractional Calculus and Applied Analysis, 2023, 26 : 111 - 146
  • [3] S-Asymptotically Periodic Solutions for Time-Space Fractional Evolution Equation
    Qiang Li
    Lishan Liu
    Mei Wei
    [J]. Mediterranean Journal of Mathematics, 2021, 18
  • [4] S-Asymptotically Periodic Solutions for Time-Space Fractional Evolution Equation
    Li, Qiang
    Liu, Lishan
    Wei, Mei
    [J]. MEDITERRANEAN JOURNAL OF MATHEMATICS, 2021, 18 (04)
  • [5] Effects of bounded space in the solutions of time-space fractional diffusion equation
    Allami, M. H.
    Shokri, B.
    [J]. PHYSICAL REVIEW E, 2010, 82 (06):
  • [6] A family of solutions of the time-space fractional longitudinal wave equation
    Liu, Jian-Gen
    Feng, Yi-Ying
    [J]. COMMUNICATIONS IN THEORETICAL PHYSICS, 2023, 75 (07)
  • [7] Difference numerical solutions for time-space fractional advection diffusion equation
    Zhang, Fangfang
    Gao, Xiaoyang
    Xie, Zhaokun
    [J]. BOUNDARY VALUE PROBLEMS, 2019,
  • [8] Difference numerical solutions for time-space fractional advection diffusion equation
    Fangfang Zhang
    Xiaoyang Gao
    Zhaokun Xie
    [J]. Boundary Value Problems, 2019
  • [9] Blow-up of Solutions for a Time-space Fractional Evolution System
    Yong Qiang XU
    Zhong TAN
    [J]. Acta Mathematica Sinica,English Series, 2013, (06) : 1067 - 1074
  • [10] Blow-up of solutions for a time-space fractional evolution system
    Xu, Yong Qiang
    Tan, Zhong
    [J]. ACTA MATHEMATICA SINICA-ENGLISH SERIES, 2013, 29 (06) : 1067 - 1074
12345