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Linear and Quasilinear Parabolic Problems - gebunden oder broschiert

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[EAN: 9783764351144], Neubuch, [PU: Birkhäuser Basel], DIFFERENZIALRECHNUNG MATHEMATIK HÖHERE BOUNDARYVALUEPROBLEM DISTRIBUTION FOURIERTRANSFORM FUNCTIONALANALYSIS PDE SOBOLEVSPACE SYSTEM… Mehr…

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Linear and Quasilinear Parabolic Problems : Abstract Linear Theory - gebunden oder broschiert

1995, ISBN: 3764351144

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Herbert Amann:
Linear and Quasilinear Parabolic Problems - gebunden oder broschiert

1995, ISBN: 3764351144

[EAN: 9783764351144], Neubuch, [PU: Springer], pp. 380, Books

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Linear and Quasilinear Parabolic Problems

This treatise gives an exposition of the functional analytical approach to quasilinear parabolic evolution equations, developed to a large extent by the author during the last 10 years. This approach is based on the theory of linear nonautonomous parabolic evolution equations and on interpolation-extrapolation techniques. It is the only general method that applies to noncoercive quasilinear parabolic systems under nonlinear boundary conditions.The present first volume is devoted to a detailed study of nonautonomous linear parabolic evolution equations in general Banach spaces. It contains a careful exposition of the constant domain case, leading to some improvements of the classical Sobolevskii-Tanabe results. It also includes recent results for equations possessing constant interpolation spaces. In addition, systematic presentations of the theory of maximal regularity in spaces of continuous and Hölder continuous functions, and in Lebesgue spaces, are given. It includes related recent theorems in the field of harmonic analysis in Banach spaces and on operators possessing bounded imaginary powers. Lastly, there is a complete presentation of the technique of interpolation-extrapolation spaces and of evolution equations in those spaces, containing many new results.

Detailangaben zum Buch - Linear and Quasilinear Parabolic Problems


EAN (ISBN-13): 9783764351144
ISBN (ISBN-10): 3764351144
Gebundene Ausgabe
Taschenbuch
Erscheinungsjahr: 1995
Herausgeber: Birkhäuser Basel
372 Seiten
Gewicht: 0,730 kg

Buch in der Datenbank seit 2007-05-28T19:50:20+02:00 (Berlin)
Detailseite zuletzt geändert am 2023-11-15T19:28:25+01:00 (Berlin)
ISBN/EAN: 3764351144

ISBN - alternative Schreibweisen:
3-7643-5114-4, 978-3-7643-5114-4
Alternative Schreibweisen und verwandte Suchbegriffe:
Autor des Buches: herbert amann, gely, herbert may, amann per, herbert hille
Titel des Buches: linear and quasilinear parabolic problems volume abstract linear theory


Daten vom Verlag:

Autor/in: Herbert Amann
Titel: Monographs in Mathematics; Linear and Quasilinear Parabolic Problems - Volume I: Abstract Linear Theory
Verlag: Birkhäuser; Springer Basel
338 Seiten
Erscheinungsjahr: 1995-03-27
Basel; CH
Gewicht: 1,560 kg
Sprache: Englisch
181,89 € (DE)
186,99 € (AT)
201,00 CHF (CH)
POD
XXXV, 338 p.

BB; Analysis; Hardcover, Softcover / Mathematik/Analysis; Mathematische Analysis, allgemein; Verstehen; Boundary value problem; Distribution; Fourier transform; Functional Analysis; PDE; Sobolev space; Systems and Control; convolution; harmonic analysis; Functional Analysis; Systems Theory, Control; Calculus of Variations and Optimal Control; Optimization; Analysis; Functional Analysis; Systems Theory, Control; Calculus of Variations and Optimization; Funktionalanalysis und Abwandlungen; Kybernetik und Systemtheorie; Optimierung; BC; EA

Notations and Conventions.- 1 Topological Spaces.- 2 Locally Convex Spaces.- 3 Complexifications.- 4 Unbounded Linear Operators.- 5 General Conventions.- I Generators and Interpolation.- 1 Generators of Analytic Semigroups.- 1.1 Properties of Linear Operators.- 1.2 The Class H(E1E0).- 1.3 Perturbation Theorems.- 1.4 Spectral Estimates.- 1.5 Compact Perturbations.- 1.6 Matrix Generators.- 2 Interpolation Functors.- 2.1 Definitions.- 2.2 Interpolation Inequalities.- 2.3 Retractions.- 2.4 Standard Interpolation Functors.- 2.5 Continuous Injections.- 2.6 Duality Properties.- 2.7 Compactness.- 2.8 Reiteration Theorems.- 2.9 Fractional Powers and Interpolation.- 2.10 Semigroups and Interpolation.- 2.11 Admissible Interpolation Functors.- II Cauchy Problems and Evolution Operators.- 1 Linear Cauchy Problems.- 1.1 Hölder Spaces.- 1.2 Existence and Regularity Theorems.- 2 Parabolic Evolution Operators.- 2.1 Basic Properties.- 2.2 Determining Integral Equations.- 3 Linear Volterra Integral Equations.- 3.1 Weakly Singular Kernels.- 3.2 Resolvent Kernels.- 3.3 Singular Gronwall Inequalities.- 4 Existence of Evolution Operators.- 4.1 A Class of Parameter Integrals.- 4.2 Semigroup Estimates.- 4.3 Construction of Evolution Operators.- 4.4 The Main Result.- 4.5 Solvability of the Cauchy Problem.- 5 Stability Estimates.- 5.1 Estimates for Evolution Operators.- 5.2 Continuity Properties of Mild Solutions.- 5.3 Holder Estimates.- 5.4 Boundedness of Mild Solutions.- 6 Invariance and Positivity.- 6.1 Yosida Approximations.- 6.2 Approximations of Evolution Operators.- 6.3 Invariance.- 6.4 Orderings and Positivity.- III Maximal Regularity.- 1 General Principles.- 1.1 Sobolev Spaces.- 1.2 Absolutely Continuous Functions.- 1.3 Generalized Solutions.- 1.4 Trace Spaces.- 1.5 Pairs of Maximal Regularity.- 1.6 Stability.- 2 Maximal Hölder Regularity.- 2.1 Singular Holder Spaces.- 2.2 Semigroup Estimates.- 2.3 Trace Spaces.- 2.4 Estimates for KA.- 2.5 Maximal Regularity.- 2.6 Nonautonomous Problems.- 3 Maximal Continuous Regularity.- 3.1 Necessary Conditions.- 3.2 Higher Order Interpolation Spaces.- 3.3 Estimates for KA.- 3.4 Maximal Regularity.- 4 Maximal Sobolev Regularity.- 4.1 Temperate Distributions.- 4.2 Fourier Transforms and Convolutions.- 4.3 The Hilbert Transform.- 4.4 UMD Spaces and Fourier Multipliers.- 4.5 Properties of UMD Spaces.- 4.6 Fractional Powers.- 4.7 Bounded Imaginary Powers.- 4.8 Perturbation Theorems.- 4.9 Sums of Closed Operators.- 4.10 Maximal Regularity.- IV Variable Domains.- 1 Higher Regularity.- 1.1 Properties of Differentiable Functions.- 1.2 General Solvability Results for Cauchy Problems.- 1.3 Estimates for Evolution Operators.- 1.4 Evolution Operators on Interpolation Spaces.- 1.5 The Cauchy Problem.- 2 Constant Interpolation Spaces.- 2.1 Semigroup and Convergence Estimates.- 2.2 Assumptions and Consequences.- 2.3 Construction of Evolution Operators.- 2.4 Estimates for Evolution Operators.- 2.5 The Cauchy Problem.- 2.6 Abstract Boundary Value Problems.- 3 Maximal Regularity.- 3.1 Abstract Initial Boundary Value Problems.- 3.2 Isomorphism Theorems.- V Scales of Banach Spaces.- 1 Banach Scales.- 1.1 General Concepts.- 1.2 Power Scales.- 1.3 Extrapolation Spaces.- 1.4 Dual Scales.- 1.5 Interpolation-Extrapolation Scales.- 2 Evolution Equations in Banach Scales.- 2.1 Semigroups in Interpolation-Extrapolation Scales.- 2.2 Parabolic Evolution Equations in Banach Scales.- 2.3 Duality.- 2.4 Approximation Theorems.- 2.5 Final Value Problems.- 2.6 Weak Solutions and Duality.- 2.7 Positivity.- 2.8 General Evolution Equations.- List of Symbols.

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