Series: Springer Monographs in Mathematics
1st Edition., 2010, 778 p. 20 illus., 10 in color., Hardcover
ISBN: 978-0-387-87711-2
Due: May 25, 2010
Provides a thorough introduction to theory and methods of evolutionary Karman plate theory
Explores critical nonlinearities and nonlinear damping, developing relevant tools
Presents new and original results in the field
Includes extensive background material
The main goal of this book is to discuss and present results on well-posedness, regularity and long-time behavior of non-linear dynamic plate (shell) models described by von Karman evolutions. While many of the results presented here are the outgrowth of very recent studies by the authors, including a number of new original results here in print for the first time - authors have provided a comprehensive and reasonably self-contained exposition of the general topic outlined above. This includes supplying all the functional analytic framework along with the function space theory as pertinent in the study of nonlinear plate models. While von Karman evolutions are the object under considerations, the methods developed transcendent this specific model and may be applied to many other equations, systems which exhibit similar hyperbolic or ultra-hyperbolic behavior (e.g. Berger's plate equations, Mindlin-Timoschenko systems, Kirchhoff-Boussinesq equations etc. In order to achieve a reasonable level of generality, the theoretical tools presented in the book are fairly abstract and tuned to general classes of second-order (in time) evolution equations, which are defined on abstract Banach spaces. The mathematical machinery needed to establish well-posedness of these dynamical systems, their regularity and long-time behavior is developed at the abstract level, where the needed hypotheses are axiomatized. This approach allows to look at von Karman evolutions as just one of the examples of a much broader class of evolutions. The generality of the approach and techniques developed are applicable (as shown in the book) to many other dynamics sharing certain rather general properties.
Well-posedness.- Evolutionary Equations.- Von Karman models with rotational
forces.- Von Karman equations without rotational intertia.- Thermoelasticity
of Plates.- Structural Acoustic Problems and Plates in a Potential Flow
of Gas.- Attractors for evolutionary equations.- Long-time behaviour of
second order abstract equations.- Plates with Internal Damping.- Plates
with Boundary Damping.- Thermoelasticity.- Composite Wave/Plate Systems.-
Inertial Manifolds for von Karman Plate Equations.
Series: Lecture Notes in Mathematics, Vol. 1993
1st Edition., 2010, X, 160 p., Softcover
ISBN: 978-3-642-12152-4
Due: May 2010
The author has been a central player in new developments of this area
This book is a much needed exposition
This volume deals with problems in the structure theory of separable infinite-dimensional Banach spaces, with a central focus on universality problems. This topic goes back to the beginnings of the field and appears in Banach's classical monograph. The novelty of the approach lies in the fact that the answers to a number of basic questions are based on techniques from Descriptive Set Theory. Although the book is oriented on proofs of several structural theorems, in the main text readers will also find a detailed exposition of numerous gintermediateh results which are interesting in their own right and have proven to be useful in other areas of Functional Analysis. Moreover, several well-known results in the geometry of Banach spaces are presented from a modern perspective.
1. Basic concepts.- 2. The space of separable Banach spaces.- 3. The l2 Baire sum.- 4. Amalgamated spaces.- 5. Zippin's embedding Theorem.- 6. The Bourgain-Pisier construction.- 7. Strongly bounded classes.
Series: Lecture Notes in Mathematics, Vol. 1994
1st Edition., 2010, XII, 200 p., Softcover
ISBN: 978-3-642-12229-3
Due: May 2010
Includes a systematic description of various Bessel functions of the first kind
Contains a special chapter on geometric properties of generalized Bessel functions of the first kind
A large number of functional inequalities involving Bessel and hypergeometric functions are collected
In this volume we study the generalized Bessel functions of the first kind by using a number of classical and new findings in complex and classical analysis. Our aim is to present interesting geometric properties and functional inequalities for these generalized Bessel functions. Moreover, we extend many known inequalities involving circular and hyperbolic functions to Bessel and modified Bessel functions.
1. Introduction and preliminary results.- 2. Geometric properties of generalized Bessel functions.- 3. Inequalities involving Bessel and hypergeometric functions.- 4. Appendix.- References.- Index.
Series: Lecture Notes in Mathematics, Vol. 1995
1st Edition., 2010, XII, 282 p., Softcover
ISBN: 978-3-642-12412-9
Due: May 2010
Physically motivated, mathematically challenging and timely Relatively few results are available in the field The results described in this book are certainly novel and original
The goal of this monograph is to address the issue of the global controllability of partial differential equations in the context of multiplicative (or bilinear) controls, which enter the model equations as coefficients. The mathematical models we examine include the linear and nonlinear parabolic and hyperbolic PDE's, the Schrodinger equation, and coupled hybrid nonlinear distributed parameter systems modeling the swimming phenomenon. The book offers a new, high-quality and intrinsically nonlinear methodology to approach the aforementioned highly nonlinear controllability problems.
1. Introduction.- Part I Multiplicative Controllability of Parabolic Equations.- 2. Global Nonnegative Controllability of the 1-D Semilinear Parabolic Equation.- 3. Multiplicative Controllability of the Semilinear Parabolic Equation: A Qualitative Approach.- 4. The Case of the Reaction-Diffusion Term Satisfying Newtonfs Law.- Part II Multiplicative Controllability of Hyperbolic Equations.- 6. Controllability Properties of a Vibrating String with Variable Axial Load and Damping Gain.- 7. Controllability Properties of a Vibrating String with Variable Axial Load Only.- 8. Reachability of Nonnegative Equilibrium States for the Semilinear Vibrating String.- 9. The 1-D Wave and Rod Equations Governed by Controls That Are Time-Dependent Only.- Part III Controllability for Swimming Phenomenon.- 10. Introduction.- 11. A gBasich 2-D Swimming Model.- 12. The Well-Posedness of a 2-D Swimming Model.- 13. Geometric Aspects of Controllability for a Swimming Phenomenon.- 14. Local Controllability for a Swimming Model.- 15. Global Controllability for a hRowingh Swimming Model.- Part IV Multiplicative Controllability Properties of the Schrodinger Equation.- 16. Multiplicative Controllability for the Schrodinger Equation.
Series: Lecture Notes in Mathematics, Vol. 2000
1st Edition., 2010, X, 190 p., Softcover
ISBN: 978-3-642-12247-7
Due: May 27, 2010
The style is excellent and pedagogical The author is first class analyst Accessible to a mathematical audience at the beginning graduate level as well as to physicists and theoretical chemists with a comparable mathematical background The contents requires no deeper knowledge of the theory of partial differential equations, of functional analysis, or quantum theory.
The electronic Schrodinger equation describes the motion of N-electrons under Coulomb interaction forces in a field of clamped nuclei. The solutions of this equation, the electronic wave functions, depend on 3N variables, with three spatial dimensions for each electron. Approximating these solutions is thus inordinately challenging, and it is generally believed that a reduction to simplified models, such as those of the Hartree-Fock method or density functional theory, is the only tenable approach. This book seeks to show readers that this conventional wisdom need not be ironclad: the regularity of the solutions, which increases with the number of electrons, the decay behavior of their mixed derivatives, and the antisymmetry enforced by the Pauli principle contribute properties that allow these functions to be approximated with an order of complexity which comes arbitrarily close to that for a system of one or two electrons. The text is accessible to a mathematical audience at the beginning graduate level as well as to physicists and theoretical chemists with a comparable mathematical background and requires no deeper knowledge of the theory of partial differential equations, functional analysis, or quantum theory.
Series: Operator Theory: Advances and Applications
Subseries: Linear Operators and Linear Systems, Vol. 208
2nd Printing., 2010, 300 p., Hardcover
ISBN: 978-3-0346-0508-3
Due: June 2010
Important step towards establishing a bridge between nonlinear semigroup theory, functional and differential equations and geometric function theory
Self-contained presentation with a complete account of definitions, proofs and references
Presentation of relevant prerequisites from iteration theory, fixed point theory and univalent functions
Linearization models for discrete and continuous time dynamical systems are the driving forces for modern geometric function theory and composition operator theory on function spaces.
This book focuses on a systematic survey and detailed treatment of linearization models for one-parameter semigroups, Schroderfs and Abelfs functional equations, and various classes of univalent functions which serve as intertwining mappings for nonlinear and linear semigroups. These topics are applicable to the study of problems in complex analysis, stochastic and evolution processes and approximation theory.
Preface.- 1 Geometric Background.- 2 Dynamical Approach.- 3 Starlike Functions with Respect to a Boundary Point.- 4 Spirallike Functions with Respect to a Boundary Point.- 5 Koenigfs Type Starlike and Spirallike Functions.- 6 Rigidity of Holomorphic Mappings and Commuting Semigroups.- 7 Asymptotic Behavior of One-parameter Semigroups.- 8 Backward Flow Invariant Domains for Semigroups.- 9 Appendices.- Bibliography.- Index.