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Partial differential equations with discrete and distributed state-dependent delays. (English) Zbl 1178.35370
Summary: This work is an 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.

MSC:
35R10 Partial functional-differential equations
35B41 Attractors
35B40 Asymptotic behavior of solutions to PDEs
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