Buch, Englisch, 354 Seiten, Format (B × H): 178 mm x 254 mm, Gewicht: 530 g
Reihe: Chapman & Hall/CRC Research Notes in Mathematics Series
Buch, Englisch, 354 Seiten, Format (B × H): 178 mm x 254 mm, Gewicht: 530 g
Reihe: Chapman & Hall/CRC Research Notes in Mathematics Series
ISBN: 978-0-8493-0685-3
Verlag: Chapman and Hall/CRC
In this masterful study, the author sets forth a unique treatment of the stability and instability of the periodic equilibria of partial differential equations as they relate to the notion of direct integrals. His results, and to a large extent his methods are new. Although he aims this work at theory rather than applications, once the theoretical framework is built, applications emerge with ease.
Readers with some basis in functional analysis-notably semigroups-and measure theory can strengthen their background through its introductory material on direct integrals and its proofs worked out in detail. In Stability, Instability and Direct Integrals, applied and pure mathematicians and theoretical physicists can discover from an acknowledged innovator the most recent results of research in this active and expanding field.
Fachgebiete
- Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
- Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Computeranwendungen in der Mathematik
- Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
Weitere Infos & Material
PrefaceNotations and PreliminariesIntroductionReaction-Diffusion Systems on an Infinite PlateReaction-Diffusion Systems on an Infinite PlateThe Laplacian on an infinite plateFloquet-Periodic Functionsq-Periodic FunctionsFourier SeriesThe q-Periodic LaplacianThe Periodic CaseDirect IntegralsDirect Integrals of Hilbert SpacesDirect Integrals of OperatorsSpectral ConsiderationsRelations Between Measure and SpectraHolomorphic Families of OperatorsProof of Lemma 4.2CommentsNavier-Stokes on an Infinite PlateNavier-Stokes on an Infinite PlateThe Stokes Operator on the Infinite PlateFourier ExpansionsThe Projection Operator PThe Floquet-Periodic Stokes OperatorParity ConsiderationsTraces Expressed in Terms of Fourier SeriesThe q-Periodic Stokes OperatorComputational AspectsSome Auxiliary LemmasThe Regularity ProofThe Proof of Theorem 6.2 (a)Discussion of the Regularity ProofSome Consequences of the Regularity ProofThe q-Periodic Projection OperatorA Different Definition of EqThe q-Periodic Neumann ProblemThe q-Periodic Projection OperatorStokes Operator, Pressure and Direct IntegralsPreparatory StepsProof of Theorem 8.1Proof of Theorem 8.2Parity ReconsideredSpectral Theory and Direct IntegralsSome Holomorphic Families of OperatorsFamilies of ResolventsLocal Spectral RelationsThe Corners: Preliminary RemarksThe Corners and their Influence on the SpectrumRelationship with the Periodic SpectrumThe Principle of Linearized InstabilityRemarks on the Principle of Linearized InstabilityReal Elements in the Space of Direct IntegralsA Topological InterpretationConstruction of a Family of Projection OperatorsDirect Integral Representation of a Projection OperatorRemarksThe Principle of Linearized Instability: Nonlinear PartThe Nonlinear TermsFurther Remarks on Fractional PowersFixed Points of an Integral EquationInstability: Proof of Theorem 10.2**Instability via Complex Projection OperatorsFurther RemarksThe Boussinesq EquationsThe Boussinesq EquationsRemarks in the Infinite PlateRemarks in the q-Periodic SettingRemarks on Direct IntegralsRemarks on Spectral TheoryRemarks on the Principle of Linearized InstabilityBibliographyIndex
