125,062 research outputs found
Hyperbolicity of linear partial differential equations with delay
Robust hyperbolicity and stability results for linear partial differential
equations with delay will be given and, as an application, the effect of small
delays to the asymptotic properties of feedback systems will be analyzed
On the Relation of Delay Equations to First-Order Hyperbolic Partial Differential Equations
This paper establishes the equivalence between systems described by a single
first-order hyperbolic partial differential equation and systems described by
integral delay equations. System-theoretic results are provided for both
classes of systems (among them converse Lyapunov results). The proposed
framework can allow the study of discontinuous solutions for nonlinear systems
described by a single first-order hyperbolic partial differential equation
under the effect of measurable inputs acting on the boundary and/or on the
differential equation. An illustrative example shows that the conversion of a
system described by a single first-order hyperbolic partial differential
equation to an integral delay system can simplify considerably the solution of
the corresponding robust feedback stabilization problem.Comment: 32 pages, submitted for possible publication to ESAIM COC
Spectrum and amplitude equations for scalar delay-differential equations with large delay
The subject of the paper are scalar delay-differential equations with
large delay. Firstly, we describe the asymptotic properties of the spectrum
of linear equations. Using these properties, we classify possible types of
destabilization of steady states. In the limit of large delay, this
classification is similar to the one for parabolic partial differential
equations. We present a derivation and error estimates for amplitude
equations, which describe universally the local behavior of scalar
delay-differential equations close to the destabilization threshold
Existence, positivity and stability for a nonlinear model of cellular proliferation
In this paper, we investigate a system of two nonlinear partial differential
equations, arising from a model of cellular proliferation which describes the
production of blood cells in the bone marrow. Due to cellular replication, the
two partial differential equations exhibit a retardation of the maturation
variable and a temporal delay depending on this maturity. We show that this
model has a unique solution which is global under a classical Lipschitz
condition. We also obtain the positivity of the solutions and the local and
global stability of the trivial equilibrium
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