A condition on delay for differential equations with discrete state-dependent delay

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• 作者：Alexander V. Rezounenko^a ; ^{rezounenko@univer.kharkov.ua"" rel=""nofollow}
• 关键词：Partial functional differential equation ; State-dependent delay ; Well-posedness ; Global attractor
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2012
• 出版时间：1 January 2012
• 年：2012
• 卷：385
• 期：1
• 页码：506-516
• 全文大小：210 K

文摘

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 functions C. The dynamical system is constructed in C and the existence of a compact global attractor is proved.