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arXiv · 0801.4715

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

Alexander V. Rezounenko
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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.

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Alexander V. Rezounenko. 2008-01-30. Differential equations with discrete state-dependent delay: uniqueness and well-posedness in the space of continuous functions. https://doi.org/10.1016/j.na.2008.08.006

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