A condition on delay for differential equations with discrete state-dependent delay
Analysis of PDEs
2014-12-02 v1 Dynamical Systems
Abstract
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 Analysis: Theory, Methods and Applications, 70 (11) (2009), 3978-3986] is developed. We propose and study a state-dependent analogue of the condition which is sufficient for the well-posedness of the corresponding initial value problem on the whole space of continuous functions . The dynamical system is constructed in and the existence of a compact global attractor is proved.
Cite
@article{arxiv.1011.4488,
title = {A condition on delay for differential equations with discrete state-dependent delay},
author = {A. V. Rezounenko},
journal= {arXiv preprint arXiv:1011.4488},
year = {2014}
}