GLOBAL SOLUTIONS AND BLOWING-UP SOLUTIONS FOR A NONAUTONOMOUS AND NONLOCAL IN SPACE REACTION-DIFFUSION SYSTEM WITH DIRICHLET BOUNDARY CONDITIONS

被引：1
作者：
Ceballos-Lira, Marcos J. [1 ]
Perez, Aroldo [1 ]
机构：
[1] Univ Juarez Autonoma Tabasco, Div Acad Ciencias Basicas, AP 24, Cunduacan 86690, Tabasco, Mexico
来源：
FRACTIONAL CALCULUS AND APPLIED ANALYSIS | 2020年 / 23卷 / 04期
关键词：
reaction-diffusion systems; finite time blow up; fractional Laplacian; Dirichlet problem; ultracontractive semigroup; killed process; HEAT KERNEL; CRITICAL EXPONENTS; PARABOLIC-SYSTEM; FUJITA TYPE; ULTRACONTRACTIVITY; NONEXISTENCE; EXISTENCE; EQUATIONS;
D O I：
10.1515/fca-2020-0054
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We give sufficient conditions for global existence and finite time blow up of positive solutions for a nonautonomous weakly coupled system with distinct fractional diffusions and Dirichlet boundary conditions. Our approach is based on the intrinsic ultracontractivity property of the semigroups associated to distinct fractional diffusions and the study of blow up of a particular system of nonautonomus delay differential equations.
引用
收藏
页码：1025 / 1053
页数：29
相关论文
共 31 条
  • [1] On Nonlinear Nonlocal Systems of Reaction Diffusion Equations
    Ahmad, B.
    Alhothuali, M. S.
    Alsulami, H. H.
    Kirane, M.
    Timoshin, S.
    [J]. ABSTRACT AND APPLIED ANALYSIS, 2014,
  • [2] Global and nonglobal solutions of a system of nonautonomous semilinear equations with ultracontractive Levy generators
    Alfredo Lopez-Mimbela, Jose
    Perez, Aroldo
    [J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2015, 423 (01) : 720 - 733
  • [3] A NECESSARY AND SUFFICIENT CONDITIONS FOR EXISTENCE OF NON NEGATIVE SOLUTIONS FOR SOME SEMILINEAR NON MONOTONE EQUATIONS
    BARAS, P
    PIERRE, M
    [J]. ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 1985, 2 (03): : 185 - 212
  • [4] Blow-up for some nonautonomous differential equations and inequalities with deviating arguments
    Ceballos-Lira, Marcos J.
    Perez, Aroldo
    [J]. BOLETIN DE LA SOCIEDAD MATEMATICA MEXICANA, 2020, 26 (02): : 459 - 475
  • [5] CEBALLOS-LIRA MARCOS JOSÍAS, 2019, Rev.colomb.mat., V53, P57
  • [6] DIRICHLET HEAT KERNEL ESTIMATES FOR Δα/2 + Δβ/2
    Chen, Zhen-Qing
    Kim, Panki
    Song, Renming
    [J]. ILLINOIS JOURNAL OF MATHEMATICS, 2010, 54 (04) : 1357 - 1392
  • [7] SHARP HEAT KERNEL ESTIMATES FOR RELATIVISTIC STABLE PROCESSES IN OPEN SETS
    Chen, Zhen-Qing
    Kim, Panki
    Song, Renming
    [J]. ANNALS OF PROBABILITY, 2012, 40 (01) : 213 - 244
  • [8] Heat kernel estimates for the Dirichlet fractional Laplacian
    Chen, Zhen-Qing
    Kim, Panki
    Song, Renming
    [J]. JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY, 2010, 12 (05) : 1307 - 1329
  • [9] Intrinsic ultracontractivity and conditional gauge for symmetric stable processes
    Chen, ZQ
    Song, RM
    [J]. JOURNAL OF FUNCTIONAL ANALYSIS, 1997, 150 (01) : 204 - 239
  • [10] ULTRACONTRACTIVITY AND THE HEAT KERNEL FOR SCHRODINGER-OPERATORS AND DIRICHLET LAPLACIANS
    DAVIES, EB
    SIMON, B
    [J]. JOURNAL OF FUNCTIONAL ANALYSIS, 1984, 59 (02) : 335 - 395
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