Reaction-diffusion systems governed by non-autonomous forms

被引：2
|
作者：
Arendt, Wolfgang [1 ]
Dier, Dominik [1 ]
机构：
[1] Univ Ulm, Inst Appl Anal, D-89069 Ulm, Germany
来源：
JOURNAL OF DIFFERENTIAL EQUATIONS | 2018年 / 264卷 / 10期
关键词：
Reaction-diffusion equations; Sesquilinear forms; Non-autonomous evolution equations; Maximal regularity; CONVEX-SETS; INVARIANCE; DOMINATION;
D O I：
10.1016/j.jde.2018.01.035
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We consider a semilinear problem u' (t) + A(t)u(t) = f (u(t)), u(0) = u(0), where A(t) is associated with a non-autonomous form a(t, ., .). Using an invariance principle for closed, convex sets in the underlying Hilbert space we find conditions for global solutions. This can be applied to reaction diffusion systems on L-2(Omega)(N). Our point is that the forms a(t, ., .) need only to be submarkovian to carry over invariance of the (scalar) reaction equation to the reaction-diffusion system. (C) 2018 Published by Elsevier Inc.
引用
收藏
页码：6362 / 6379
页数：18
相关论文
共 50 条
  • [1] Attractors of non-autonomous reaction-diffusion equations
    Song, Haitao
    Ma, Shan
    Zhong, Chengkui
    [J]. NONLINEARITY, 2009, 22 (03) : 667 - 681
  • [2] Attractors of non-autonomous reaction-diffusion equations in Lp
    Song, Haitao
    Zhong, Chengkui
    [J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2008, 68 (07) : 1890 - 1897
  • [3] Kolmogorov ε-entropy estimates for the uniform attractors of non-autonomous reaction-diffusion systems
    Vishik, MI
    Chepyzhov, VV
    [J]. SBORNIK MATHEMATICS, 1998, 189 (1-2) : 235 - 263
  • [4] Stability analysis of non-autonomous reaction-diffusion systems: the effects of growing domains
    Madzvamuse, Anotida
    Gaffney, Eamonn A.
    Maini, Philip K.
    [J]. JOURNAL OF MATHEMATICAL BIOLOGY, 2010, 61 (01) : 133 - 164
  • [5] REGULARITY OF PULLBACK ATTRACTORS FOR NON-AUTONOMOUS STOCHASTIC COUPLED REACTION-DIFFUSION SYSTEMS
    Yin, Jinyan
    Li, Yangrong
    Gu, Anhui
    [J]. JOURNAL OF APPLIED ANALYSIS AND COMPUTATION, 2017, 7 (03): : 884 - 898
  • [6] On evolution equations governed by non-autonomous forms
    El-Mennaoui, Omar
    Laasri, Hafida
    [J]. ARCHIV DER MATHEMATIK, 2016, 107 (01) : 43 - 57
  • [7] Stability analysis of non-autonomous reaction-diffusion systems: the effects of growing domains
    Anotida Madzvamuse
    Eamonn A. Gaffney
    Philip K. Maini
    [J]. Journal of Mathematical Biology, 2010, 61 : 133 - 164
  • [8] On evolution equations governed by non-autonomous forms
    Omar El-Mennaoui
    Hafida Laasri
    [J]. Archiv der Mathematik, 2016, 107 : 43 - 57
  • [9] Dynamics and regularity for non-autonomous reaction-diffusion equations with anomalous diffusion
    Yan, Xingjie
    Wang, Shubin
    Yang, Xin-Guang
    Zhang, Junzhao
    [J]. ASYMPTOTIC ANALYSIS, 2023, 132 (3-4) : 495 - 517
  • [10] NON-AUTONOMOUS REACTION-DIFFUSION EQUATIONS WITH VARIABLE EXPONENTS AND LARGE DIFFUSION
    Fernandes, Antonio Carlos
    Goncalves, Marcela Carvalho
    Simsen, Jacson
    [J]. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2019, 24 (04): : 1485 - 1510
12345