Layers and spikes in non-homogeneous bistable reaction-diffusion equations

Authors:
Shangbing Ai, Xinfu Chen and Stuart P. Hastings

Journal:
Trans. Amer. Math. Soc. **358** (2006), 3169-3206

MSC (2000):
Primary 35K57

Published electronically:
February 20, 2006

MathSciNet review:
2216263

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Abstract: We study , where , , and is sufficiently small, on an interval with boundary conditions at . All solutions with an independent number of oscillations are analyzed. Existence of complicated patterns of layers and spikes is proved, and their Morse index is determined. It is observed that the results extend to with and also to an infinite interval.

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Additional Information

**Shangbing Ai**

Affiliation:
Department of Mathematical Sciences, University of Alabama at Huntsville, Huntsville, Alabama 35899

Email:
ais@email.uah.edu

**Xinfu Chen**

Affiliation:
Department of Mathematics, University of Pittsburgh, Pittsburgh, Pennsylvania 15260

Email:
xinfu@pitt.edu

**Stuart P. Hastings**

Affiliation:
Department of Mathematics, University of Pittsburgh, Pittsburgh, Pennsylvania 15260

Email:
sph@pitt.edu

DOI:
https://doi.org/10.1090/S0002-9947-06-03834-7

Received by editor(s):
April 17, 2002

Received by editor(s) in revised form:
September 1, 2004

Published electronically:
February 20, 2006

Additional Notes:
The second author thanks the National Science Foundation Grant DMS–0203991 for their support.

Article copyright:
© Copyright 2006
American Mathematical Society