## Merging traveling waves for the porous-Fisher's equation

Publication
, Journal Article

Witelski, TP

Published in: Applied Mathematics Letters

January 1, 1995

We study a reaction-diffusion equation model for population dynamics. By focusing on the diffusive behavior expected in a population that seeks to avoid over-crowding, we derive a nonlinear-diffusion porous-Fisher's equation. Using explicit traveling wave solutions, initially-separated, expanding populations are studied as they first coalesce. The nonlinear interactions of the merging populations are examined using perturbation theory and the method of matched asymptotic expansions. Results are also extended to the axisymmetric case. © 1995.

### Duke Scholars

## Published In

Applied Mathematics Letters

## DOI

## ISSN

0893-9659

## Publication Date

January 1, 1995

## Volume

8

## Issue

4

## Start / End Page

57 / 62

## Related Subject Headings

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

### Citation

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Chicago

ICMJE

MLA

NLM

Witelski, T. P. (1995). Merging traveling waves for the porous-Fisher's equation.

*Applied Mathematics Letters*,*8*(4), 57–62. https://doi.org/10.1016/0893-9659(95)00047-TWitelski, T. P. “Merging traveling waves for the porous-Fisher's equation.”

*Applied Mathematics Letters*8, no. 4 (January 1, 1995): 57–62. https://doi.org/10.1016/0893-9659(95)00047-T.Witelski TP. Merging traveling waves for the porous-Fisher's equation. Applied Mathematics Letters. 1995 Jan 1;8(4):57–62.

Witelski, T. P. “Merging traveling waves for the porous-Fisher's equation.”

*Applied Mathematics Letters*, vol. 8, no. 4, Jan. 1995, pp. 57–62.*Scopus*, doi:10.1016/0893-9659(95)00047-T.Witelski TP. Merging traveling waves for the porous-Fisher's equation. Applied Mathematics Letters. 1995 Jan 1;8(4):57–62.

## Published In

Applied Mathematics Letters

## DOI

## ISSN

0893-9659

## Publication Date

January 1, 1995

## Volume

8

## Issue

4

## Start / End Page

57 / 62

## Related Subject Headings

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