## Parabolic behavior of a hyperbolic delay equation

Publication
, Journal Article

Laurent, T; Rider, B; Reed, M

Published in: SIAM Journal on Mathematical Analysis

March 1, 2006

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 → ∞. 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 → ∞. © 2006 Society for Industrial and Applied Mathematics.

### Duke Scholars

## Published In

SIAM Journal on Mathematical Analysis

## DOI

## ISSN

0036-1410

## Publication Date

March 1, 2006

## Volume

38

## Issue

1

## Start / End Page

1 / 15

## Related Subject Headings

- Applied Mathematics
- 4904 Pure mathematics
- 4901 Applied mathematics
- 0102 Applied Mathematics
- 0101 Pure Mathematics

### Citation

APA

Chicago

ICMJE

MLA

NLM

Laurent, T., Rider, B., & Reed, M. (2006). Parabolic behavior of a hyperbolic delay equation.

*SIAM Journal on Mathematical Analysis*,*38*(1), 1–15. https://doi.org/10.1137/040611422Laurent, T., B. Rider, and M. Reed. “Parabolic behavior of a hyperbolic delay equation.”

*SIAM Journal on Mathematical Analysis*38, no. 1 (March 1, 2006): 1–15. https://doi.org/10.1137/040611422.Laurent T, Rider B, Reed M. Parabolic behavior of a hyperbolic delay equation. SIAM Journal on Mathematical Analysis. 2006 Mar 1;38(1):1–15.

Laurent, T., et al. “Parabolic behavior of a hyperbolic delay equation.”

*SIAM Journal on Mathematical Analysis*, vol. 38, no. 1, Mar. 2006, pp. 1–15.*Scopus*, doi:10.1137/040611422.Laurent T, Rider B, Reed M. Parabolic behavior of a hyperbolic delay equation. SIAM Journal on Mathematical Analysis. 2006 Mar 1;38(1):1–15.

## Published In

SIAM Journal on Mathematical Analysis

## DOI

## ISSN

0036-1410

## Publication Date

March 1, 2006

## Volume

38

## Issue

1

## Start / End Page

1 / 15

## Related Subject Headings

- Applied Mathematics
- 4904 Pure mathematics
- 4901 Applied mathematics
- 0102 Applied Mathematics
- 0101 Pure Mathematics