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Spectral theory for forward nonautonomous parabolic equations and applications. (English) Zbl 1274.35253
Mallet-Paret, John (ed.) et al., Infinite dimensional dynamical systems. Collected papers of the international conference, Toronto, Canada, September 24–28, 2008. New York, NY: Springer; Toronto: Fields Institute for Research in Mathematical Sciences (ISBN 978-1-4614-4522-7/hbk; 978-1-4614-4523-4/ebook). Fields Institute Communications 64, 57-99 (2012).
Summary: We introduce the concept of the principal spectrum for linear forward nonautonomous parabolic partial differential equations. The principal spectrum is a nonempty compact interval. Fundamental properties of the principal spectrum for forward nonautonomous equations are investigated. The paper concludes with applications of the principal spectrum theory to the problem of uniform persistence in some population growth models.
For the entire collection see [Zbl 1253.37006].

MSC:
35P15 Estimates of eigenvalues in context of PDEs
35K15 Initial value problems for second-order parabolic equations
35P05 General topics in linear spectral theory for PDEs
35K55 Nonlinear parabolic equations
37B55 Topological dynamics of nonautonomous systems
92D25 Population dynamics (general)
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