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

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

2005-03-22

arxiv.org/abs/math/0503470v1

Journal of Mathematical Analysis and Applications. Volume 326, Issue 2, (15 February 2007), Pages 1031-1045.

Mathematics

Dynamical Systems

17 pages

Scientific paper

10.1016/j.jmaa.2006.03.049

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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