Spectral Properties of Integral Operators in Problems of Interface Dynamics and Metastability

A. De Masi, E. Olivieri, E. Presutti

1998, v.4, Issue 1, 27-112


In this paper we study some integral operators that are obtained by linearizations of a non-local evolution equation for a non-conserved order parameter describing the phase of a fluid. We prove a Perron - Frobenius theorem by showing that there is an isolated, simple, maximal eigenvalue larger than 1 with a positive eigenvector and that the rest of the spectrum is strictly contained in the unit ball. Such properties are responsible for the existence of invariant, attractive, unstable one-dimensional manifolds under the full, non linear evolution. This part of the analysis and the application to interface dynamics and metastability will be carried out in separate papers.

Keywords: Perron - Frobenius theorem,interfaces,stationary fronts,instantons


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