Existence and dynamics of quasilinear parabolic systems with time delays
Existence and dynamics of quasilinear parabolic systems with time delays
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DOI：
10.1016/j.jde.2015.01.010
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发表时间：
2015-05
影响因子：
2.4
通讯作者：
C. Pao;W. Ruan
中科院分区：
文献类型：
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作者：
C. Pao;W. Ruan
本文研究了一类拟线性抛物型耦合方程组，在反应函数中考虑了时滞的影响。系统中的偏微分算子可能是退化的，反应函数具有一定的混合拟单调性质，其中包括拟单调非减函数。本文的目的是证明抛物系统整体解的存在唯一性，相应椭圆组的正拟解或极大极小解的存在性，以及抛物系统解相对于椭圆组的拟解或极大极小解的渐近行为。给出了应用于数学、生物学和生态学的三个反应扩散模型，其中扩散系数依赖于密度并且是退化的。与密度无关的扩散相比，这种依赖于密度的简并扩散导致了依赖于时间的解的一些有趣的明显的渐近行为。
This paper is concerned with a coupled system of quasilinear parabolic equations where the effect of time delays is taken into consideration in the reaction functions of the system. The partial differential operators in the system may be degenerate and the reaction functions possess some mixed quasimonotone property, including quasimonotone nondecreasing functions. The aim of the paper is to show the existence and uniqueness of a global solution to the parabolic system, the existence of positive quasisolutions or maximal–minimal solutions of the corresponding elliptic system, and the asymptotic behavior of the solution of the parabolic system in relation to the quasisolutions or maximal–minimal solutions of the elliptic system. Applications are given to three reaction–diffusion models arising from mathematical biology and ecology where the diffusion coefficients are density dependent and are degenerate. This degenerate density-dependent diffusion leads to some interesting distinct asymptotic behavior of the time-dependent solution when compared with density-independent diffusion.