Series: Springer INdAM Series, Vol. 2
2013, VIII, 300 p. 11 illus.
Hardcover
ISBN 978-88-470-2840-1
Due: January 31, 2013
The survey articles provide excellent introductions for interested researchers
Potential readers belong to several areas of mathematics
The set of original papers covers a wide range of up-to-date and hot topics in the study of PDE's
The study of qualitative aspects of PDE's has always attracted much attention from the early beginnings. More recently, once basic issues about PDE's, such as existence, uniqueness and stability of solutions, have been understood quite well, research on topological and/or geometric properties of their solutions has become more intense. The study of these issues is attracting the interest of an increasing number of researchers and is now a broad and well-established research area, with contributions that often come from experts from disparate areas of mathematics, such as differential and convex geometry, functional analysis, calculus of variations, mathematical physics, to name a few.
This volume collects a selection of original results and informative surveys by a group of international specialists in the field, analyzes new trends and techniques and aims at promoting scientific collaboration and stimulating future developments and perspectives in this very active area of research.
Goro Akagi, Stability and instability of group invariant asymptotic profiles for fast diffusion equations.- Elvise Berchio, A family of Hardy-Rellich type inequalities involving the L2-norm of the Hessian matrices.- Massimiliano Bianchini and Paolo Salani, Power concavity for solutions of nonlinear elliptic problems in convex domains.- Lorenzo Brasco and Rolando Magnanini, The heart of a convex set.- Giulio Ciraolo, A viscosity equation for minimizers of a class of very degenerate elliptic functionals.- Adele Ferone, Kato's inequality in the half space: an alternative proof and relative improvements.- Ilaria Fragala, Filippo Gazzola and Jimmy Lamboley, Sharp bounds for the p-torsion of convex planar domains.- Giovanni Franzina and Enrico Valdinoci, Geometric analysis of fractional phase transition interfaces.- Antonio Greco, Existence of solutions to some classical variational problems.- Norihisa Ikoma, Existence of minimizers for some coupled nonlinear Schrodinger equations.- Kazuhiro Ishige and Yoshitsugu Kabeya, Decay rate of Lq norms of critical Schrodinger heat semigroups.- Shuichi Jimbo, Hadamard variation for electromagnetic frequencies.- Toru Kan, Global structure of the solution set for a semilinear elliptic problem related to the Liouville equation on an annulus.- Anna Mercaldo, A priori estimates and comparison principle for some nonlinear elliptic equations.- Takeyuki Nagasawa, Existence and uniqueness of the n-dimensional Helfrich flow.- Bernhard Ruf and Federica Sani, Ground states for elliptic equations in R2 with exponential critical growth.- Shigeru Sakaguchi, Stationary level surfaces and Liouville-type theorems characterizing hyperplanes.- Futoshi Takahashi, Nonexistence of multi-bubble solutions for a higher order mean field on equation on convex domains.
Series: Applied Mathematical Sciences, Vol. 183
2013, 2013, X, 533 p. 12 illus., 1 in color.
Hardcover
ISBN 978-1-4614-5974-3
Due: December 28, 2012
The methods presented in the book can be applied to a wide range of domains in nonlinear analysis
Some very recent research results are presented along with more classical ones
The first chapter of the book presents, with details, the derivation of the equations of fluid mechanics
The objective of this self-contained book is two-fold. First, the reader is introduced to the modelling and mathematical analysis used in fluid mechanics, especially concerning the Navier-Stokes equations which is the basic model for the flow of incompressible viscous fluids. Authors introduce mathematical tools so that the reader is able to use them for studying many other kinds of partial differential equations, in particular nonlinear evolution problems.
The background needed are basic results in calculus, integration, and functional analysis. Some sections certainly contain more advanced topics than others. Nevertheless, the authorsf aim is that graduate or PhD students, as well as researchers who are not specialized in nonlinear analysis or in mathematical fluid mechanics, can find a detailed introduction to this subject.
Preface.- Contents.- The equations of fluid mechanics.- Analysis tools.- Sobolev spaces.- Steady Stokes equations.- Navier-Stokes equations for homogeneous fluids.- Nonhomogeneous fluids.- Boundary conditions modeling.- Classic differential operators.- Thermodynamics supplement.- References.- Index.-
Series: Graduate Texts in Mathematics, Vol. 264
2013, 2013, XIV, 594 p. 14 illus., 8 in color.
Hardcover
ISBN 978-1-4471-4819-7
Due: January 31, 2013
A self-contained in-depth introduction to functional analysis and the related fields of optimal control and the calculus of variations that is unique in its coverage
Written in a lively and engaging style by a leading specialist
Includes a short course on optimization and nonsmooth analysis
Gives complete proofs of advanced versions of the Pontryagin maximum principle that appear for the first time in a textbook
Contains hundreds of exercises of an original nature, with solutions or hints in many cases
Functional analysis owes much of its early impetus to problems that arise in the calculus of variations. In turn, the methods developed there have been applied to optimal control, an area that also requires new tools, such as nonsmooth analysis. This self-contained textbook gives a complete course on all these topics. It is written by a leading specialist who is also a noted expositor.
This book provides a thorough introduction to functional analysis and includes many novel elements as well as the standard topics. A short course on nonsmooth analysis and geometry completes the first half of the book whilst the second half concerns the calculus of variations and optimal control. The author provides a comprehensive course on these subjects, from their inception through to the present. A notable feature is the inclusion of recent, unifying developments on regularity, multiplier rules, and the Pontryagin maximum principle, which appears here for the first time in a textbook. Other major themes include existence and Hamilton-Jacobi methods.
The many substantial examples, and the more than three hundred exercises, treat such topics as viscosity solutions, nonsmooth Lagrangians, the logarithmic Sobolev inequality, periodic trajectories, and systems theory. They also touch lightly upon several fields of application: mechanics, economics, resources, finance, control engineering.
Functional Analysis, Calculus of Variations and Optimal Control is intended to support several different courses at the first-year or second-year graduate level, on functional analysis, on the calculus of variations and optimal control, or on some combination. For this reason, it has been organized with customization in mind. The text also has considerable value as a reference. Besides its advanced results in the calculus of variations and optimal control, its polished presentation of certain other topics (for example convex analysis, measurable selections, metric regularity, and nonsmooth analysis) will be appreciated by researchers in these and related fields.
Normed Spaces.- Convex sets and functions.- Weak topologies.- Convex analysis.- Banach spaces.- Lebesgue spaces.- Hilbert spaces.- Additional exercises for Part I.- Optimization and multipliers.- Generalized gradients.- Proximal analysis.- Invariance and monotonicity.- Additional exercises for Part II.- The classical theory.- Nonsmooth extremals.- Absolutely continuous solutions.- The multiplier rule.- Nonsmooth Lagrangians.- Hamilton-Jacobi methods.- Additional exercises for Part III.- Multiple integrals.- Necessary conditions.- Existence and regularity.- Inductive methods.- Differential inclusions.- Additional exercises for Part IV.
Series: Sources in the History of Mathematics and Physical Sciences
2013, 2013, XVI, 808 p. 36 illus., 1 in color.
Hardcover
ISBN 978-1-4614-5724-4
Due: February 15, 2013
Presents the first complete account of the development of the work and ideas of Cauchy, Riemann, and Weierstrass in complex function theory
Analyzes the history of elliptic function theory and its implications for the development of complex function theory as the first full-length treatment of the interactions between these two fields
Examines the interaction of complex function theory with other fields, including number theory, mechanics, and differential equations?
Hidden Harmony?Geometric Fantasies describes the history of complex function theory from its origins to 1914, when the essential features of the modern theory were in place. It is the first history of mathematics devoted to complex function theory, and it draws on a wide range of published and unpublished sources. In addition to an extensive and detailed coverage of the three founders of the subject?Cauchy, Riemann, and Weierstrass?it looks at the contributions of great mathematicians from dfAlembert to Poincare, and Laplace to Weyl.
Select chapters examine the rise and importance of elliptic function theory, differential equations in the complex domain, geometric function theory, and the early years of complex function theory in several variables. Unique emphasis has been placed on the creation of a textbook tradition in complex analysis by considering some seventy textbooks in nine different languages. This book is not a mere sequence of disembodied results and theories, but offers a comprehensive picture of the broad cultural and social context in which the main players lived and worked by paying attention to the rise of mathematical schools and of contrasting national traditions.
This work is unrivaled for its breadth and depth, both in the core theory and its implications for other fields of mathematics. It is a major resource for professional mathematicians as well as advanced undergraduate and graduate students and anyone studying complex function theory.
.-List of Figures.-Introduction.-1. Elliptic Functions.-2. From real to complex.-3. Cauch.-4. Elliptic integrals.-5. Riemann.- 6. Weierstrass.-7. Differential equations.-8. Advanced topics.-9. Several variables.-10. Textbooks
Series: Frontiers in Mathematics
2013, X, 272 p.
Softcover
ISBN 978-3-0348-0576-6
Due: March 2013
Well-written systematic and comprehensive exposition
Presents a solution of the Aizerman ] Myshkis problem
Develops the Hill method for functional differential equations with period coefficients
Differential equations with delay naturally occur in various applications, such as control systems, viscoelasticity, mechanics, nuclear reactors, distributed networks, heat flows, neural networks, combustion, interaction of species, microbiology, learning models, epidemiology, physiology, and many others. This book systematically investigates the stability of linear as well as nonlinear vector differential equations with delay and equations with causal mappings. It presents explicit conditions for exponential, absolute and input-to-state stabilities. These stability conditions are mainly formulated in terms of the determinants and eigenvalues of auxiliary matrices dependent on a parameter; the suggested approach allows us to apply the well-known results of the theory of matrices. In addition, solution estimates for the considered equations are established which provide the bounds for regions of attraction of steady states.
The main methodology presented in the book is based on a combined usage of the recent norm estimates for matrix-valued functions and the following methods and results: the generalized Bohl-Perron principle and the integral version of the generalized Bohl-Perron principle; the freezing method; the positivity of fundamental solutions. A significant part of the book is devoted to the Aizerman-Myshkis problem and generalized Hill theory of periodic systems.
The book is intended not only for specialists in the theory of functional differential equations and control theory, but also for anyone with a sound mathematical background interested in their various applications.
Preface.- 1. Preliminaries.- 2. Some Results of the Matrix Theory.- 3. General Linear Systems.- 4. Time-Invariant Linear Systems with Delay.- ?5. Properties of Characteristic Values.- 6. Equations Close to Autonomous and Ordinary Differential Ones.- 7. Periodic Systems.- 8. Linear Equations with Oscillating Coefficients.- 9. Linear Equations with Slowly Varying Coefficients.- 10. Nonlinear Vector Equations.- 11. Scalar Nonlinear Equations.- 12. Forced Oscillations in Vector Semi-Linear Equations.- 13. Steady States of Differential Delay Equations.- 14. Multiplicative Representations of Solutions.- Appendix A. The General Form of Causal Operators.- Appendix B. Infinite Block Matrices.- Bibliography.- Index.
To Be Published 7th November 2012
2,536 pages
Hardback: 978-0-415-55764-1
The science of complexity is concerned with the study of complex, adaptive systems. Its insights have in recent decades been applied with gusto by social scientists and other thinkers.
As research in and around the application of complexity science flourishes as never before, this new five-volume collection from Routledge meets the need for an authoritative reference work to make sense of a rapidly growing?and ever more complex?corpus of literature. Edited by leading scholars, the collection gathers foundational and canonical work, together with innovative and cutting-edge applications and interventions.
With a full index, together with new introductions to each volume, which place the collected material in its historical and intellectual context, Complexity is an essential work of reference. The collection will be particularly useful as an essential database allowing scattered and often fugitive material to be easily located. It will also be welcomed as a crucial tool permitting rapid access to less familiar?and sometimes overlooked?texts. For researchers, students, practitioners, and policy-makers, it is as a vital one-stop research and pedagogic resource