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

作者：Rezounenko Alexander V^*

来源：Journal of Mathematical Analysis and Applications, 2012, 385(1): 506-516.

DOI：10.1016/j.jmaa.2011.06.070

• Partial functional differential equation
• State-dependent delay
• Well-posedness
• Global attractor

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) 3978-398] 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.

• 出版日期2012-1-1