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Spectral Theory for Forward Nonautonomous Parabolic Equations and Applications

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Book cover Infinite Dimensional Dynamical Systems

Part of the book series: Fields Institute Communications ((FIC,volume 64))

Abstract

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.

The second-named author was partially supported by NSF grant DMS–0907752

Mathematics Subject Classification (2010): Primary 35K15, 35P05; Secondary 35K55, 35P15, 37B55, 92D25

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Author information

Authors and Affiliations

  1. Institute of Mathematics and Computer Science, Wrocław University of Technology, Wybrzeże Wyspiańskiego 27, PL-50-370, Wrocław, Poland

    Janusz Mierczyński

  2. Department of Mathematics and Statistics, Auburn University, Auburn, AL, 36849, USA

    Wenxian Shen

Authors
  1. Janusz Mierczyński
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  2. Wenxian Shen
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Correspondence to Janusz Mierczyński .

Editor information

Editors and Affiliations

  1. Division of Applied Mathematics, Brown University, Providence, RI, USA

    John Mallet-Paret

  2. Department of Mathematics and Statistics, York University, Toronto, ON, Canada

    Jianhong Wu  & Huaiping Zhu  & 

  3. Georgia Institute of Technology, School of Mathematics, Atlanta, GA, USA

    Yingfei Yi

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Mierczyński, J., Shen, W. (2013). Spectral Theory for Forward Nonautonomous Parabolic Equations and Applications. In: Mallet-Paret, J., Wu, J., Yi, Y., Zhu, H. (eds) Infinite Dimensional Dynamical Systems. Fields Institute Communications, vol 64. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-4523-4_2

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