Differential equations with discrete state-dependent delay: Uniqueness and well-posedness in the space of continuous functions

✍ Scribed by Alexander V. Rezounenko

• Publisher: Elsevier Science
• Year: 2009
• Tongue: English
• Weight: 617 KB
• Volume: 70
• Category: Article
• ISSN: 0362-546X
• DOI: 10.1016/j.na.2008.08.006

✦ Synopsis

Partial differential equations with discrete (concentrated) state-dependent delays in the space of continuous functions are investigated. In general, the corresponding initial value problem is not well-posed. So we find an additional assumption on the state-dependent delay function to guarantee the well-posedness. For the constructed dynamical system we study the long-time asymptotic behavior and prove the existence of a compact global attractor.