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Two models of partial differential equations with discrete and distributed state-dependent delays

Alexander V. Rezounenko
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Abstract

This work is the first attempt to treat partial differential equations with discrete (concentrated) state-dependent delay. The main idea is to approximate the discrete delay term by a sequence of distributed delay terms (all with state-dependent delays). We study local existence and long-time asymptotic behavior of solutions and prove that the model with distributed delay has a global attractor while the one with discrete delay possesses the trajectory attractor.

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Alexander V. Rezounenko. 2005-03-22. Two models of partial differential equations with discrete and distributed state-dependent delays. https://doi.org/10.1016/j.jmaa.2006.03.049

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