# Parabolic Behavior of a Hyperbolic Delay Equation

@article{Laurent2006ParabolicBO,
title={Parabolic Behavior of a Hyperbolic Delay Equation},
author={Thomas Laurent and Brian Rider and Michael C. Reed},
journal={SIAM J. Math. Anal.},
year={2006},
volume={38},
pages={1-15}
}
• Published 1 August 2006
• Mathematics
• SIAM J. Math. Anal.
It is shown that the fundamental solution of a hyperbolic partial differential equation with time delay has a natural probabilistic structure, i.e., is approximately Gaussian, as $t \rightarrow \infty.$ The proof uses ideas from the DeMoivre proof of the central limit theorem. It follows that solutions of the hyperbolic equation look approximately like solutions of a diffusion equation with constant convection as $t \rightarrow \infty.$

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## References

SHOWING 1-10 OF 10 REFERENCES

• Mathematics
• 1992
Preface. 1. Models. 2. General Theory. 3. Stability of Retarded Differential Equations. 4. Stability of Neutral Type Functional Differential Equations. 5. Stability of Stochastic Functional
• Mathematics
Chaos
• 1992
The resulting mathematical model is a nonlinear first-order partial differential equation for the cell density u(t,x) in which there is retardation in both temporal (t) and maturation variables (x), and contains three parameters.
• Biology
• 2003
An analysis is provided for a model of the blood production system based on a cell population structured by a continuous variable corresponding to the maturity of individual cells. Cell maturity is
• Mathematics
• 1976
Preface to the Classics Edition Preface 1. Weak convergence of probability measures and uniformity classes 2. Fourier transforms and expansions of characteristic functions 3. Bounds for errors of
II. Differentiation II.2. Examples of differentiation. The case of one variable (n = 1). II.2.3. Pseudofunctions. Hadamard finite part. We calculate the derivative of a function f(x) which is equal
Thank you for reading an introduction to probability theory and its applications vol 2. As you may know, people have look numerous times for their favorite novels like this an introduction to

• 1993