Spectral Theory for Random and Nonautonomous Parabolic Equations and Applications: 1st Edition (Hardback) book cover

Spectral Theory for Random and Nonautonomous Parabolic Equations and Applications

1st Edition

By Janusz Mierczynski, Wenxian Shen

Chapman and Hall/CRC

336 pages

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pub: 2008-03-24
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Description

Providing a basic tool for studying nonlinear problems, Spectral Theory for Random and Nonautonomous Parabolic Equations and Applications focuses on the principal spectral theory for general time-dependent and random parabolic equations and systems. The text contains many new results and considers existing results from a fresh perspective.

Taking a clear, unified, and self-contained approach, the authors first develop the abstract general theory in the framework of weak solutions, before turning to cases of random and nonautonomous equations. They prove that time dependence and randomness do not reduce the principal spectrum and Lyapunov exponents of nonautonomous and random parabolic equations. The book also addresses classical Faber–Krahn inequalities for elliptic and time-periodic problems and extends the linear theory for scalar nonautonomous and random parabolic equations to cooperative systems. The final chapter presents applications to Kolmogorov systems of parabolic equations.

By thoroughly explaining the spectral theory for nonautonomous and random linear parabolic equations, this resource reveals the importance of the theory in examining nonlinear problems.

Table of Contents

Introduction. Fundamental Properties in the General Setting. Spectral Theory in the General Setting. Spectral Theory in Nonautonomous and Random Cases. Influence of Spatial-Temporal Variations and the Shape of Domain. Cooperative Systems of Parabolic Equations. Applications to Kolmogorov Systems of Parabolic Equations. References. Index.

About the Authors

Mierczynski, Janusz; Shen, Wenxian

About the Series

Monographs and Surveys in Pure and Applied Mathematics

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Subject Categories

BISAC Subject Codes/Headings:
MAT000000
MATHEMATICS / General
MAT007000
MATHEMATICS / Differential Equations
MAT029010
MATHEMATICS / Probability & Statistics / Bayesian Analysis