On a nonlinear time-fractional cable equation

被引：0
作者：
Jleli, Mohamed [1 ]
Samet, Bessem [1 ]
机构：
[1] King Saud Univ, Coll Sci, Dept Math, Riyadh 11451, Saudi Arabia
来源：
AIMS MATHEMATICS | 2024年 / 9卷 / 09期
关键词：
time-fractional cable equation; weak solution; nonexistence; Caputo fractional derivative; BLOWING-UP SOLUTIONS; GLOBAL-SOLUTIONS; NONEXISTENCE; DIFFUSION; SYSTEM;
D O I：
10.3934/math.20241146
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
A nonlinear time-fractional cable equation posed on the interval (0,1) , 1) under a homogeneous Dirichlet boundary condition is investigated in this work. The considered equation reflects the anomalous electro-diffusion ff usion in nerve cells. Using nonlinear capacity estimates specifically adapted to the considered problem, we establish sufficient ffi cient conditions for the nonexistence of weak solutions.
引用
收藏
页码：23584 / 23597
页数：14
相关论文
共 17 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 TIME-SPACE FRACTIONAL EVOLUTION EQUATION
    Fino, Ahmad Z.
    Kirane, Mokhtar
    [J]. QUARTERLY OF APPLIED MATHEMATICS, 2012, 70 (01) : 133 - 157
  • [3] NONEXISTENCE OF GLOBAL SOLUTIONS FOR TIME FRACTIONAL WAVE EQUATIONS IN AN EXTERIOR DOMAIN
    He, Jia Wei
    [J]. JOURNAL OF INTEGRAL EQUATIONS AND APPLICATIONS, 2023, 35 (01) : 11 - 26
  • [4] Implicit compact difference schemes for the fractional cable equation
    Hu, Xiuling
    Zhang, Luming
    [J]. APPLIED MATHEMATICAL MODELLING, 2012, 36 (09) : 4027 - 4043
  • [5] NONEXISTENCE FOR TIME-FRACTIONAL WAVE INEQUALITIES ON RIEMANNIAN MANIFOLDS
    Jleli, Mohamed
    Samet, Bessem
    [J]. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S, 2023, 16 (06): : 1517 - 1536
  • [6] Multi-term time-fractional diffusion equation and system: mild solutions and critical exponents
    Kassymov, Aidyn
    Tokmagambetov, Niyaz
    Torebek, Berikbol
    [J]. PUBLICATIONES MATHEMATICAE-DEBRECEN, 2022, 100 (3-4): : 295 - 321
  • [7] Kilbas A, 2006, Theory and Applications of Fractional Differential Equations, P204
  • [8] Critical exponents of Fujita type for certain evolution equations and systems with spatio-temporal fractional derivatives
    Kirane, M
    Laskri, Y
    Tatar, NE
    [J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2005, 312 (02) : 488 - 501
  • [9] Blowing-up solutions to two-times fractional differential equations
    Kirane, Mokhtar
    Kadem, Abdelouhab
    Debbouche, Amar
    [J]. MATHEMATISCHE NACHRICHTEN, 2013, 286 (17-18) : 1797 - 1804
  • [10] The profile of blowing-up solutions to a nonlinear system of fractional differential equations
    Kirane, Mokhtar
    Malik, Salman A.
    [J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2010, 73 (12) : 3723 - 3736
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