A condition on delay for differential equations with discrete state-dependent delay
A condition on delay for differential equations with discrete state-dependent delay
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DOI：
10.1016/j.jmaa.2011.06.070
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发表时间：
2010-11
期刊：
影响因子：
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通讯作者：
A. Rezounenko
中科院分区：
文献类型：
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作者：
A. Rezounenko
研究了具有离散状态依赖时滞的抛物型微分方程。该方法基于在[A. V. Rezounenko，Differential equations with discrete state-dependent delay：unique and well-posedness in the space of continuous functions，Nonlinear Anal. 70（11）（2009）3978-3986]。本文提出并研究了在整个连续函数空间C上相应初值问题适定性的充分条件的一个类似条件。在C中构造了动力系统，证明了系统的紧全局吸引子的存在性。
Parabolic differential equations with discrete state-dependent delay are studied. The approach, based on an additional condition on the delay function introduced in [A.V. Rezounenko, Differential equations with discrete state-dependent delay: uniqueness and well-posedness in the space of continuous functions, Nonlinear Anal. 70 (11) (2009) 3978–3986] is developed. We propose and study an analogue of the condition which is sufficient for the well-posedness of the corresponding initial value problem on the whole space of continuous functionsC. The dynamical system is constructed inCand the existence of a compact global attractor is proved.