Estimates for the principal spectrum point for certain time-dependent parabolic operators

Authors:
V. Hutson, W. Shen and G. T. Vickers

Journal:
Proc. Amer. Math. Soc. **129** (2001), 1669-1679

MSC (2000):
Primary 35K20, 35P15; Secondary 92D25

DOI:
https://doi.org/10.1090/S0002-9939-00-05808-1

Published electronically:
November 2, 2000

MathSciNet review:
1814096

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Non-autonomous parabolic equations are discussed. The periodic case is considered first and an estimate for the principal periodic-parabolic eigenvalue is obtained by relating the original problem to the elliptic one obtained by time-averaging. It is then shown that an analogous bound may be obtained for the principal spectrum point in the almost periodic case. These results have applications to the stability of nonlinear systems and hence, for example, to permanence for biological systems.

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Additional Information

**V. Hutson**

Affiliation:
School of Mathematics and Statistics, The University of Sheffield, Sheffield S3 7RH, United Kingdom

Email:
v.hutson@sheffield.ac.uk

**W. Shen**

Affiliation:
Department of Mathematics, Auburn University, Auburn, Alabama 36849

Email:
ws@cam.auburn.edu

**G. T. Vickers**

Affiliation:
School of Mathematics and Statistics, The University of Sheffield, Sheffield S3 7RH, United Kingdom

Email:
g.vickers@sheffield.ac.uk

DOI:
https://doi.org/10.1090/S0002-9939-00-05808-1

Received by editor(s):
September 7, 1999

Published electronically:
November 2, 2000

Additional Notes:
The second author was partially supported by NSF grant DMS-9704245.

Communicated by:
David S. Tartakoff

Article copyright:
© Copyright 2000
American Mathematical Society