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Author:   Herbert Amann ,  B Scarpellini (University of Basel, Basel, Switzerland)
Publisher:   Taylor & Francis Ltd
Imprint:   Chapman & Hall/CRC
Volume:   402
Dimensions:   Width: 17.80cm , Height: 2.00cm , Length: 25.40cm
Weight:   0.530kg
ISBN:  

9780849306853

ISBN 10:   084930685
Pages:   354
Publication Date:   29 January 1999
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Out of Print
Availability:   Out of stock  

Table of Contents

Preface Notations and Preliminaries Introduction Reaction-Diffusion Systems on an Infinite Plate Reaction-Diffusion Systems on an Infinite Plate The Laplacian on an infinite plate Floquet-Periodic Functions q-Periodic Functions Fourier Series The q-Periodic Laplacian The Periodic Case Direct Integrals Direct Integrals of Hilbert Spaces Direct Integrals of Operators Spectral Considerations Relations Between Measure and Spectra Holomorphic Families of Operators Proof of Lemma 4.2 Comments Navier-Stokes on an Infinite Plate Navier-Stokes on an Infinite Plate The Stokes Operator on the Infinite Plate Fourier Expansions The Projection Operator P The Floquet-Periodic Stokes Operator Parity Considerations Traces Expressed in Terms of Fourier Series The q-Periodic Stokes Operator Computational Aspects Some Auxiliary Lemmas The Regularity Proof The Proof of Theorem 6.2 (a) Discussion of the Regularity Proof Some Consequences of the Regularity Proof The q-Periodic Projection Operator A Different Definition of Eq The q-Periodic Neumann Problem The q-Periodic Projection Operator Stokes Operator, Pressure and Direct Integrals Preparatory Steps Proof of Theorem 8.1 Proof of Theorem 8.2 Parity Reconsidered Spectral Theory and Direct Integrals Some Holomorphic Families of Operators Families of Resolvents Local Spectral Relations The Corners: Preliminary Remarks The Corners and their Influence on the Spectrum Relationship with the Periodic Spectrum The Principle of Linearized Instability Remarks on the Principle of Linearized Instability Real Elements in the Space of Direct Integrals A Topological Interpretation Construction of a Family of Projection Operators Direct Integral Representation of a Projection Operator Remarks The Principle of Linearized Instability: Nonlinear Part The Nonlinear Terms Further Remarks on Fractional Powers Fixed Points of an Integral Equation Instability: Proof of Theorem 10.2** Instability via Complex Projection Operators Further Remarks The Boussinesq Equations The Boussinesq Equations Remarks in the Infinite Plate Remarks in the q-Periodic Setting Remarks on Direct Integrals Remarks on Spectral Theory Remarks on the Principle of Linearized Instability Bibliography Index

Reviews

introduction toreaction-diffusion systemssuitable for a newcomer to the field. Mathematical Reviews, 2000j

""…introduction to…reaction-diffusion systems…suitable for a newcomer to the field."" Mathematical Reviews , 2000j

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