Differential equations with discrete state-dependent delay: Uniqueness and well-posedness in the space of continuous functions
By A. Rezounenko. 2008
52 citations recorded by the source corpus.
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.
Subfields: Computer Networks and Communications, Control and Systems Engineering, Public Health, Environmental and Occupational Health
View Paper: https://www.semanticscholar.org/paper/ebe00056a855e0fda7601cc348d25ff651e161d9
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In Computer Networks and Communications
In Control and Systems Engineering
In Public Health, Environmental and Occupational Health
Citations in the corpus
- On differentiability of solutions with respect to parameters in neutral differential equations with state-dependent delays (2011, methodology): “Similar assumption is used for SD-NFDEs in [17], see condition (g1) in [34,35], and for PDEs with state-dependent delays in [30].”
- Parabolic partial differential equations with discrete state-dependent delay: Classical solutions and solution manifold (2014, methodology): “We also mention that a simple and natural additional property concerning the statedependent delay which guarantees the uniqueness of solutions in the whole space of continuous functions was proposed in [19] and generalized in [21].”