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Author : Aldo Belleni-Morante
Publisher : Oxford University Press, USA
Page : 412 pages
File Size : 47,8 Mb
Release : 1979
Category : Banach spaces
ISBN : UCAL:B4128592
Good,No Highlights,No Markup,all pages are intact, Slight Shelfwear,may have the corners slightly dented, may have slight color changes/slightly damaged spine.
Author : Philippe Clement
Publisher : CRC Press
Page : 550 pages
File Size : 54,9 Mb
Release : 1991-06-24
Category : Mathematics
ISBN : 0824785452
Proceedings of the Second International Conference on Trends in Semigroup Theory and Evolution Equations held Sept. 1989, Delft University of Technology, the Netherlands. Papers deal with recent developments in semigroup theory (e.g., positive, dual, integrated), and nonlinear evolution equations (e
Author : Belleni-morante Aldo
Publisher : World Scientific
Page : 180 pages
File Size : 46,6 Mb
Release : 1994-05-18
Category : Mathematics
ISBN : 9789813104570
This book is a simple and concise introduction to the theory of semigroups and evolution equations, both in the linear and in the semilinear case. The subject is presented by a discussion of two standard boundary value problems (from particle transport theory and from population theory), and by showing how such problems can be rewritten as evolution problems in suitable Banach spaces.Each section of the book is completed by some notes, where the relevant notions of functional analysis are explained. Some other definitions and theorems of functional analysis are discussed in the Appendices (so that the only prerequisites to read the book are classical differential and integral calculus).
Author : Delio Mugnolo
Publisher : Springer
Page : 286 pages
File Size : 50,8 Mb
Release : 2014-05-21
Category : Science
ISBN : 9783319046211
This concise text is based on a series of lectures held only a few years ago and originally intended as an introduction to known results on linear hyperbolic and parabolic equations. Yet the topic of differential equations on graphs, ramified spaces, and more general network-like objects has recently gained significant momentum and, well beyond the confines of mathematics, there is a lively interdisciplinary discourse on all aspects of so-called complex networks. Such network-like structures can be found in virtually all branches of science, engineering and the humanities, and future research thus calls for solid theoretical foundations. This book is specifically devoted to the study of evolution equations – i.e., of time-dependent differential equations such as the heat equation, the wave equation, or the Schrödinger equation (quantum graphs) – bearing in mind that the majority of the literature in the last ten years on the subject of differential equations of graphs has been devoted to elliptic equations and related spectral problems. Moreover, for tackling the most general settings - e.g. encoded in the transmission conditions in the network nodes - one classical and elegant tool is that of operator semigroups. This book is simultaneously a very concise introduction to this theory and a handbook on its applications to differential equations on networks. With a more interdisciplinary readership in mind, full proofs of mathematical statements have been frequently omitted in favor of keeping the text as concise, fluid and self-contained as possible. In addition, a brief chapter devoted to the field of neurodynamics of the brain cortex provides a concrete link to ongoing applied research.
Author : Amnon Pazy
Publisher : Springer Science & Business Media
Page : 289 pages
File Size : 54,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461255611
Since the characterization of generators of C0 semigroups was established in the 1940s, semigroups of linear operators and its neighboring areas have developed into an abstract theory that has become a necessary discipline in functional analysis and differential equations. This book presents that theory and its basic applications, and the last two chapters give a connected account of the applications to partial differential equations.
Author : Klaus-Jochen Engel,Rainer Nagel
Publisher : Springer Science & Business Media
Page : 589 pages
File Size : 47,6 Mb
Release : 2006-04-06
Category : Mathematics
ISBN : 9780387226422
This book explores the theory of strongly continuous one-parameter semigroups of linear operators. A special feature of the text is an unusually wide range of applications such as to ordinary and partial differential operators, to delay and Volterra equations, and to control theory. Also, the book places an emphasis on philosophical motivation and the historical background.
Author : Mimmo Iannelli,Gunter Lumer
Publisher : Birkhäuser
Page : 419 pages
File Size : 42,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034880855
The international conference on which the book is based brought together many of the world's leading experts, with particular effort on the interaction between established scientists and emerging young promising researchers, as well as on the interaction of pure and applied mathematics. All material has been rigorously refereed. The contributions contain much material developed after the conference, continuing research and incorporating additional new results and improvements. In addition, some up-to-date surveys are included.
Author : Brunello Terreni
Publisher : Springer Science & Business Media
Page : 426 pages
File Size : 40,6 Mb
Release : 2002
Category : Mathematics
ISBN : 3764367911
Brunello Terreni (1953-2000) was a researcher and teacher with vision and dedication. The present volume is dedicated to the memory of Brunello Terreni. His mathematical interests are reflected in 20 expository articles written by distinguished mathematicians. The unifying theme of the articles is "evolution equations and functional analysis", which is presented in various and diverse forms: parabolic equations, semigroups, stochastic evolution, optimal control, existence, uniqueness and regularity of solutions, inverse problems as well as applications. Contributors: P. Acquistapace, V. Barbu, A. Briani, L. Boccardo, P. Colli Franzone, G. Da Prato, D. Donatelli, A. Favini, M. Fuhrmann, M. Grasselli, R. Illner, H. Koch, R. Labbas, H. Lange, I. Lasiecka, A. Lorenzi, A. Lunardi, P. Marcati, R. Nagel, G. Nickel, V. Pata, M. M. Porzio, B. Ruf, G. Savaré, R. Schnaubelt, E. Sinestrari, H. Tanabe, H. Teismann, E. Terraneo, R. Triggiani, A. Yagi
Author : Gisele Ruiz Goldstein,Rainer Nagel,Silvia Romanelli
Publisher : CRC Press
Page : 440 pages
File Size : 44,5 Mb
Release : 2019-04-24
Category : Mathematics
ISBN : 9781482275957
Celebrating the work of renowned mathematician Jerome A. Goldstein, this reference compiles original research on the theory and application of evolution equations to stochastics, physics, engineering, biology, and finance. The text explores a wide range of topics in linear and nonlinear semigroup theory, operator theory, functional analysis, and li
Author : Alfredo Lorenzi,Bernhard Ruf
Publisher : Birkhäuser
Page : 404 pages
File Size : 47,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034882217
Brunello Terreni (1953-2000) was a researcher and teacher with vision and dedication. The present volume is dedicated to the memory of Brunello Terreni. His mathematical interests are reflected in 20 expository articles written by distinguished mathematicians. The unifying theme of the articles is "evolution equations and functional analysis", which is presented in various and diverse forms: parabolic equations, semigroups, stochastic evolution, optimal control, existence, uniqueness and regularity of solutions, inverse problems as well as applications. Contributors: P. Acquistapace, V. Barbu, A. Briani, L. Boccardo, P. Colli Franzone, G. Da Prato, D. Donatelli, A. Favini, M. Fuhrmann, M. Grasselli, R. Illner, H. Koch, R. Labbas, H. Lange, I. Lasiecka, A. Lorenzi, A. Lunardi, P. Marcati, R. Nagel, G. Nickel, V. Pata, M. M. Porzio, B. Ruf, G. Savaré, R. Schnaubelt, E. Sinestrari, H. Tanabe, H. Teismann, E. Terraneo, R. Triggiani, A. Yagi.
Author : Kazufumi Ito,Franz Kappel
Publisher : World Scientific
Page : 520 pages
File Size : 44,9 Mb
Release : 2002-05-24
Category : Mathematics
ISBN : 9789814488389
This book presents an approximation theory for a general class of nonlinear evolution equations in Banach spaces and the semigroup theory, including the linear (Hille–Yosida), nonlinear (Crandall–Liggett) and time-dependent (Crandall–Pazy) theorems. The implicit finite difference method of Euler is shown to generate a sequence convergent to the unique integral solution of evolution equations of the maximal monotone type. Moreover, the Chernoff theory provides a sufficient condition for consistent and stable time integration of time-dependent nonlinear equations. The Trotter–Kato theorem and the Lie–Trotter type product formula give a mathematical framework for the convergence analysis of numerical approximations of solutions to a general class of partial differential equations. This book contains examples demonstrating the applicability of the generation as well as the approximation theory. In addition, the Kobayashi–Oharu approach of locally quasi-dissipative operators is discussed for homogeneous as well as nonhomogeneous equations. Applications to the delay differential equations, Navier–Stokes equation and scalar conservation equation are given. Contents: Dissipative and Maximal Monotone OperatorsLinear SemigroupsAnalytic SemigroupsApproximation of C0-SemigroupsNonlinear Semigroups of ContractionsLocally Quasi-Dissipative Evolution EquationsThe Crandall–Pazy ClassVariational Formulations and Gelfand TriplesApplications to Concrete SystemsApproximation of Solutions for Evolution EquationsSemilinear Evolution EquationsAppendices:Some InequalitiesConvergence of Steklov MeansSome Technical Results Needed in Section 9.2 Readership: Researchers in the fields of analysis & differential equations and approximation theory. Keywords:Evolution Equations;Approximations;Euler;Trotter-Kato;Lie-Trotter;Quasi-Dissipative Operators;K and Y Kobayashi;S OharuReviews:“Ito and Kappel offer a unified presentation of the general approach for well-posedness results using abstract evolution equations, drawing from and modifying the work of K and Y Kobayashi and S Oharu … their work is not a textbook, but they explain how instructors can use various sections, or combinations of them, as a foundation for a range of courses.”Book News, Inc.
Author : A. Belleni-Morante,A. C. McBride
Publisher : John Wiley & Sons
Page : 298 pages
File Size : 40,7 Mb
Release : 1998-12-04
Category : Mathematics
ISBN : STANFORD:36105023416154
Mathematical Methods in Practice Advisory Editors Bruno Brosowski Universität Frankfurt Germany Gary F. Roach University of Strathclyde UK Volume 3 Applied Nonlinear Semigroups A. Belleni-Morante University of Florence, Italy A. C. McBride University of Strathclyde, UK In many disciplines such as physics, chemistry, biology, meteorology, electronics and economics, it is increasingly necessary to develop mathematical models that describe how the state of a system evolves with time. A useful way of studying such a model is to recast the appropriate evolution equation as an Abstract Cauchy Problem (ACP), which can then be analysed via the powerful theory of semigroups of operators. The user-friendly presentation in the book is centred on Abstract Cauchy Problems which model various processes such as particle transport,diffusion and combustion, all of which are examples of systems which evolve with time. The authors provide an introduction to the requisite concepts from functional analysis before moving on to the theory of semigroups of linear operators and their application to linear ACPs. These ideas are then applied to semilinear problems and fully nonlinear problems and it is shown how results from the linear theory can be extended. Finally, a variety of applications of practical interest are included. By leading a non-expert to the solutions of problems involving evolution equations via the theory of semigroups of operators, both linear and nonlinear, the book provides an accessible introduction to the treatment of the subject. The reader is assumed to have a basic knowledge of real analysis and vector spaces. M.Sc. and graduate students of functional analysis, applied mathematics, physics and engineering will find this an invaluable introduction to the subject.
Author : Olga A. Ladyzhenskaya
Publisher : Cambridge University Press
Page : 97 pages
File Size : 53,7 Mb
Release : 2022-06-09
Category : Mathematics
ISBN : 9781009229821
First published 1992; Re-issued 2008; Reprinted with Introduction 2022.
Author : G Lumer
Publisher : CRC Press
Page : 532 pages
File Size : 49,6 Mb
Release : 2019-04-24
Category : Medical
ISBN : 9781482277487
This volume presents a collection of lectures on linear partial differntial equations and semigroups, nonlinear equations, stochastic evolutionary processes, and evolution problems from physics, engineering and mathematical biology. The contributions come from the 6th International Conference on Evolution Equations and Their Applications in Physica
Author : Nicolae H. Pavel
Publisher : Springer
Page : 292 pages
File Size : 44,6 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540471868
This research monograph deals with nonlinear evolution operators and semigroups generated by dissipative (accretive), possibly multivalued operators, as well as with the application of this theory to partial differential equations. It shows that a large class of PDE's can be studied via the semigroup approach. This theory is not available otherwise in the self-contained form provided by these Notes and moreover a considerable part of the results, proofs and methods are not to be found in other books. The exponential formula of Crandall and Liggett, some simple estimates due to Kobayashi and others, the characterization of compact semigroups due to Brézis, the proof of a fundamental property due to Ursescu and the author and some applications to PDE are of particular interest. Assuming only basic knowledge of functional analysis, the book will be of interest to researchers and graduate students in nonlinear analysis and PDE, and to mathematical physicists.