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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
Published electronically: November 2, 2000
MathSciNet review: 1814096
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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