Differential equations with discrete state-dependent delay: uniqueness and well-posedness in the space of continuous functions
Analysis of PDEs
2014-12-16 v2 Dynamical Systems
Abstract
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.
Cite
@article{arxiv.0801.4715,
title = {Differential equations with discrete state-dependent delay: uniqueness and well-posedness in the space of continuous functions},
author = {Alexander V. Rezounenko},
journal= {arXiv preprint arXiv:0801.4715},
year = {2014}
}