Non-linear partial differential equations with discrete state-dependent delays in a metric space. (English) Zbl 1194.35488
Summary: We investigate a class of non-linear partial differential equations with discrete state-dependent delays. The existence and uniqueness of strong solutions for initial functions from a Banach space are proved. To get the well-posed initial value problem, we restrict our study to a smaller metric space, construct the dynamical system and prove the existence of a compact global attractor.
MSC:
| 35R10 | Partial functional-differential equations |
| 35B41 | Attractors |
| 35K57 | Reaction-diffusion equations |
| 35A01 | Existence problems for PDEs: global existence, local existence, non-existence |
| 35A02 | Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness |
| 37G35 | Dynamical aspects of attractors and their bifurcations |
Keywords:
partial functional differential equation; state-dependent delay; well-posedness; global attractorReferences:
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