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Functional Analytic Methods for Evolution Equations : Lecture Notes in Mathematics - Giuseppe Da Prato

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Functional Analytic Methods for Evolution Equations

By: Giuseppe Da Prato, Mimmo Iannelli (Editor), Rainer Nagel (Editor)

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Paperback | 1 September 2004

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484 Pages

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This book consists of five introductory contributions by leading mathematicians on the functional analytic treatment of evolutions equations. In particular the contributions deal with Markov semigroups, maximal L^p-regularity, optimal control problems for boundary and point control systems, parabolic moving boundary problems and parabolic nonautonomous evolution equations. The book is addressed to PhD students, young researchers and mathematicians doing research in one of the above topics.

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You Can Find This Book In

Non-Fiction Mathematics Calculus & Mathematical Analysis Differential Calculus & Equations Optimisation Linear Programming Probability & Statistics Geometry Applied Mathematics Stochastics Functional Analysis & Transforms

An Introduction to Markov Semigroups	p. 1
Gaussian Measures in Hilbert Spaces	p. 1
Gaussian Random Variables	p. 10
Markov Semigroups	p. 17
Existence and Uniqueness of Invariant Measures	p. 30
Examples of Markov Semigroups	p. 35
Bounded Perturbations of Ornstein-Uhlenbeck Generators	p. 47
Diffusion Semigroups	p. 55
References	p. 62
Maximal L_p-regularity for Parabolic Equations, Fourier Multiplier Theorems and H&Infinity; -functional Calculus	p. 65
Introduction	p. 66
An Overview: Two Approaches to Maximal Regularity	p. 69
Fourier Multiplier Theorems and Maximal Regularity	p. 83
R-boundedness	p. 83
Fourier Multiplier Theorem on R	p. 102
Fourier Multipliers on R^N	p. 120
R-bounded Sets of Classical Operators	p. 133
Elliptic Systems on Rⁿ	p. 141
Elliptic Boundary Value Problems	p. 154
Operators in Divergence Form	p. 176
The H&Infinity; -calculus	p. 196
Construction of the H&Infinity; -calculus	p. 196
First Examples for the H&Infinity; -functional Calculus	p. 208
H&Infinity; -calculus for Hilbert Space Operators	p. 219
The Operator-valued H&Infinity; -calculus and Sums of Closed Operators	p. 235
Perturbation Theorems and Elliptic Operators	p. 255
H&Infinity; -calculus for Divergence Operators	p. 268
Appendix: Fractional Powers of Sectorial Operators	p. 277
References	p. 301
Optimal Control Problems and Riccati Equations for Systems with Unbounded Controls and Partially Analytic Generators-Applications to Boundary and Point Control Problems	p. 313
Introduction	p. 313
I. Abstract Theory	p. 315
Mathematical Setting and Formulation of the Control Problem	p. 315
Abstract Results for Control Problems with Singular Estimate	p. 325
Finite Horizon Problem - Proofs	p. 328
II. Applications to Point and Boundary Control Problems	p. 343
Boundary Control Problems for Thermoelastic Plates	p. 344
Composite Beam Models with Boundary Control	p. 350
Point and Boundary Control Problems in Acoustic-structure Interactions	p. 356
References	p. 366
An Introduction to Parabolic Moving Boundary Problems	p. 371
Introduction	p. 371
The One Dimensional Case	p. 373
Basic Examples	p. 379
Weak Solutions	p. 380
The Fully Nonlinear Equations Approach	p. 382
Special Geometries	p. 390
References	p. 398
Asymptotic Behaviour of Parabolic Nonautonomous Evolution Equations	p. 401
Introduction	p. 401
Parabolic Evolution Equations	p. 404
Exponential Dichotomy	p. 417
Exponential Dichotomy of Parabolic Evolution Equations	p. 435
Inhomogeneous Problems	p. 455
Convergent Solutions for a Quasilinear Equation	p. 463
References	p. 469
Table of Contents provided by Publisher. All Rights Reserved.

Functional Analytic Methods for Evolution Equations

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