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

Hutson, V.; Shen, W.; Vickers, G.

doi:10.1090/S0002-9939-00-05808-1

Estimates for the principal spectrum point for certain time-dependent parabolic operators
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by V. Hutson, W. Shen and G. T. Vickers PDF

Proc. Amer. Math. Soc. 129 (2001), 1669-1679 Request permission

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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