Evolution Equations

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Abstract Parabolic Evolution Equations and their Applications

Author : Atsushi Yagi
Publisher : Springer Science & Business Media
ISBN 13 : 3642046312
Total Pages : 594 pages
Book Rating : 4.6/5 (42 download)

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Book Synopsis Abstract Parabolic Evolution Equations and their Applications by : Atsushi Yagi

Download or read book Abstract Parabolic Evolution Equations and their Applications written by Atsushi Yagi and published by Springer Science & Business Media. This book was released on 2009-11-03 with total page 594 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is intended to present the fundamentals of the theory of abstract parabolic evolution equations and to show how to apply to various nonlinear dif- sion equations and systems arising in science. The theory gives us a uni?ed and s- tematic treatment for concrete nonlinear diffusion models. Three main approaches are known to the abstract parabolic evolution equations, namely, the semigroup methods, the variational methods, and the methods of using operational equations. In order to keep the volume of the monograph in reasonable length, we will focus on the semigroup methods. For other two approaches, see the related references in Bibliography. The semigroup methods, which go back to the invention of the analytic se- groups in the middle of the last century, are characterized by precise formulas representing the solutions of the Cauchy problem for evolution equations. The ?tA analytic semigroup e generated by a linear operator ?A provides directly a fundamental solution to the Cauchy problem for an autonomous linear e- dU lution equation, +AU =F(t), 0

Surface Evolution Equations

Author : Yoshikazu Giga
Publisher : Springer Science & Business Media
ISBN 13 : 3764373911
Total Pages : 270 pages
Book Rating : 4.7/5 (643 download)

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Book Synopsis Surface Evolution Equations by : Yoshikazu Giga

Download or read book Surface Evolution Equations written by Yoshikazu Giga and published by Springer Science & Business Media. This book was released on 2006-03-30 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a self-contained introduction to the analytic foundation of a level set approach for various surface evolution equations including curvature flow equations. These equations are important in many applications, such as material sciences, image processing and differential geometry. The goal is to introduce a generalized notion of solutions allowing singularities, and to solve the initial-value problem globally-in-time in a generalized sense. Various equivalent definitions of solutions are studied. Several new results on equivalence are also presented. Moreover, structures of level set equations are studied in detail. Further, a rather complete introduction to the theory of viscosity solutions is contained, which is a key tool for the level set approach. Although most of the results in this book are more or less known, they are scattered in several references, sometimes without proofs. This book presents these results in a synthetic way with full proofs. The intended audience are graduate students and researchers in various disciplines who would like to know the applicability and detail of the theory as well as its flavour. No familiarity with differential geometry or the theory of viscosity solutions is required. Only prerequisites are calculus, linear algebra and some basic knowledge about semicontinuous functions.

Evolution Equations and Approximations

Author : Kazufumi Ito
Publisher : World Scientific
ISBN 13 : 9789812380265
Total Pages : 524 pages
Book Rating : 4.3/5 (82 download)

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Book Synopsis Evolution Equations and Approximations by : Kazufumi Ito

Download or read book Evolution Equations and Approximations written by Kazufumi Ito and published by World Scientific. This book was released on 2002 with total page 524 pages. Available in PDF, EPUB and Kindle. Book excerpt: Annotation Ito (North Carolina State U.) and Kappel (U. of Graz, Austria) 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. They also explore abstract approximation results for evolution equations. 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. Annotation copyrighted by Book News, Inc., Portland, OR

Semigroup Methods for Evolution Equations on Networks

Author : Delio Mugnolo
Publisher : Springer
ISBN 13 : 3319046217
Total Pages : 294 pages
Book Rating : 4.3/5 (19 download)

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Book Synopsis Semigroup Methods for Evolution Equations on Networks by : Delio Mugnolo

Download or read book Semigroup Methods for Evolution Equations on Networks written by Delio Mugnolo and published by Springer. This book was released on 2014-05-21 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Moving Interfaces and Quasilinear Parabolic Evolution Equations

Author : Jan Prüss
Publisher : Birkhäuser
ISBN 13 : 3319276980
Total Pages : 618 pages
Book Rating : 4.3/5 (192 download)

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Book Synopsis Moving Interfaces and Quasilinear Parabolic Evolution Equations by : Jan Prüss

Download or read book Moving Interfaces and Quasilinear Parabolic Evolution Equations written by Jan Prüss and published by Birkhäuser. This book was released on 2016-07-25 with total page 618 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this monograph, the authors develop a comprehensive approach for the mathematical analysis of a wide array of problems involving moving interfaces. It includes an in-depth study of abstract quasilinear parabolic evolution equations, elliptic and parabolic boundary value problems, transmission problems, one- and two-phase Stokes problems, and the equations of incompressible viscous one- and two-phase fluid flows. The theory of maximal regularity, an essential element, is also fully developed. The authors present a modern approach based on powerful tools in classical analysis, functional analysis, and vector-valued harmonic analysis. The theory is applied to problems in two-phase fluid dynamics and phase transitions, one-phase generalized Newtonian fluids, nematic liquid crystal flows, Maxwell-Stefan diffusion, and a variety of geometric evolution equations. The book also includes a discussion of the underlying physical and thermodynamic principles governing the equations of fluid flows and phase transitions, and an exposition of the geometry of moving hypersurfaces.

Nonlinear Evolution Equations - Global Behavior of Solutions

Author : Alain Haraux
Publisher : Springer
ISBN 13 : 3540385347
Total Pages : 324 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Nonlinear Evolution Equations - Global Behavior of Solutions by : Alain Haraux

Download or read book Nonlinear Evolution Equations - Global Behavior of Solutions written by Alain Haraux and published by Springer. This book was released on 2006-11-15 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Dynamical Systems and Evolution Equations

Author : John A. Walker
Publisher : Springer Science & Business Media
ISBN 13 : 1468410369
Total Pages : 244 pages
Book Rating : 4.4/5 (684 download)

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Book Synopsis Dynamical Systems and Evolution Equations by : John A. Walker

Download or read book Dynamical Systems and Evolution Equations written by John A. Walker and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book grew out of a nine-month course first given during 1976-77 in the Division of Engineering Mechanics, University of Texas (Austin), and repeated during 1977-78 in the Department of Engineering Sciences and Applied Mathematics, Northwestern University. Most of the students were in their second year of graduate study, and all were familiar with Fourier series, Lebesgue integration, Hilbert space, and ordinary differential equa tions in finite-dimensional space. This book is primarily an exposition of certain methods of topological dynamics that have been found to be very useful in the analysis of physical systems but appear to be well known only to specialists. The purpose of the book is twofold: to present the material in such a way that the applications-oriented reader will be encouraged to apply these methods in the study of those physical systems of personal interest, and to make the coverage sufficient to render the current research literature intelligible, preparing the more mathematically inclined reader for research in this particular area of applied mathematics. We present only that portion of the theory which seems most useful in applications to physical systems. Adopting the view that the world is deterministic, we consider our basic problem to be predicting the future for a given physical system. This prediction is to be based on a known equation of evolution, describing the forward-time behavior of the system, but it is to be made without explicitly solving the equation.

Evolution Equations

Author : Kaïs Ammari
Publisher : Cambridge University Press
ISBN 13 : 1108412300
Total Pages : 205 pages
Book Rating : 4.1/5 (84 download)

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Book Synopsis Evolution Equations by : Kaïs Ammari

Download or read book Evolution Equations written by Kaïs Ammari and published by Cambridge University Press. This book was released on 2018 with total page 205 pages. Available in PDF, EPUB and Kindle. Book excerpt: The proceedings of a summer school held in 2015 whose theme was long time behavior and control of evolution equations.

Evolutionary Equations with Applications in Natural Sciences

Author : Jacek Banasiak
Publisher : Springer
ISBN 13 : 3319113224
Total Pages : 505 pages
Book Rating : 4.3/5 (191 download)

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Book Synopsis Evolutionary Equations with Applications in Natural Sciences by : Jacek Banasiak

Download or read book Evolutionary Equations with Applications in Natural Sciences written by Jacek Banasiak and published by Springer. This book was released on 2014-11-07 with total page 505 pages. Available in PDF, EPUB and Kindle. Book excerpt: With the unifying theme of abstract evolutionary equations, both linear and nonlinear, in a complex environment, the book presents a multidisciplinary blend of topics, spanning the fields of theoretical and applied functional analysis, partial differential equations, probability theory and numerical analysis applied to various models coming from theoretical physics, biology, engineering and complexity theory. Truly unique features of the book are: the first simultaneous presentation of two complementary approaches to fragmentation and coagulation problems, by weak compactness methods and by using semigroup techniques, comprehensive exposition of probabilistic methods of analysis of long term dynamics of dynamical systems, semigroup analysis of biological problems and cutting edge pattern formation theory. The book will appeal to postgraduate students and researchers specializing in applications of mathematics to problems arising in natural sciences and engineering.

Harmonic Analysis Method For Nonlinear Evolution Equations, I

Author : Baoxiang Wang
Publisher : World Scientific
ISBN 13 : 9814458392
Total Pages : 298 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Harmonic Analysis Method For Nonlinear Evolution Equations, I by : Baoxiang Wang

Download or read book Harmonic Analysis Method For Nonlinear Evolution Equations, I written by Baoxiang Wang and published by World Scientific. This book was released on 2011-08-10 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph provides a comprehensive overview on a class of nonlinear evolution equations, such as nonlinear Schrödinger equations, nonlinear Klein-Gordon equations, KdV equations as well as Navier-Stokes equations and Boltzmann equations. The global wellposedness to the Cauchy problem for those equations is systematically studied by using the harmonic analysis methods.This book is self-contained and may also be used as an advanced textbook by graduate students in analysis and PDE subjects and even ambitious undergraduate students.

Semilinear Evolution Equations and Their Applications

Author : Toka Diagana
Publisher : Springer
ISBN 13 : 303000449X
Total Pages : 199 pages
Book Rating : 4.0/5 (3 download)

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Book Synopsis Semilinear Evolution Equations and Their Applications by : Toka Diagana

Download or read book Semilinear Evolution Equations and Their Applications written by Toka Diagana and published by Springer. This book was released on 2018-10-23 with total page 199 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, which is a continuation of Almost Automorphic Type and Almost Periodic Type Functions in Abstract Spaces, presents recent trends and developments upon fractional, first, and second order semilinear difference and differential equations, including degenerate ones. Various stability, uniqueness, and existence results are established using various tools from nonlinear functional analysis and operator theory (such as semigroup methods). Various applications to partial differential equations and the dynamic of populations are amply discussed. This self-contained volume is primarily intended for advanced undergraduate and graduate students, post-graduates and researchers, but may also be of interest to non-mathematicians such as physicists and theoretically oriented engineers. It can also be used as a graduate text on evolution equations and difference equations and their applications to partial differential equations and practical problems arising in population dynamics. For completeness, detailed preliminary background on Banach and Hilbert spaces, operator theory, semigroups of operators, and almost periodic functions and their spectral theory are included as well.

Existence Families, Functional Calculi and Evolution Equations

Author : Ralph DeLaubenfels
Publisher : Springer
ISBN 13 : 3540483225
Total Pages : 254 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Existence Families, Functional Calculi and Evolution Equations by : Ralph DeLaubenfels

Download or read book Existence Families, Functional Calculi and Evolution Equations written by Ralph DeLaubenfels and published by Springer. This book was released on 2006-11-15 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents an operator-theoretic approach to ill-posed evolution equations. It presents the basic theory, and the more surprising examples, of generalizations of strongly continuous semigroups known as 'existent families' and 'regularized semigroups'. These families of operators may be used either to produce all initial data for which a solution in the original space exists, or to construct a maximal subspace on which the problem is well-posed. Regularized semigroups are also used to construct functional, or operational, calculi for unbounded operators. The book takes an intuitive and constructive approach by emphasizing the interaction between functional calculus constructions and evolution equations. One thinks of a semigroup generated by A as etA and thinks of a regularized semigroup generated by A as etA g(A), producing solutions of the abstract Cauchy problem for initial data in the image of g(A). Material that is scattered throughout numerous papers is brought together and presented in a fresh, organized way, together with a great deal of new material.

Dynamics of Evolutionary Equations

Author : George R. Sell
Publisher : Springer Science & Business Media
ISBN 13 : 1475750374
Total Pages : 680 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis Dynamics of Evolutionary Equations by : George R. Sell

Download or read book Dynamics of Evolutionary Equations written by George R. Sell and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 680 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory and applications of infinite dimensional dynamical systems have attracted the attention of scientists for quite some time. This book serves as an entrée for scholars beginning their journey into the world of dynamical systems, especially infinite dimensional spaces. The main approach involves the theory of evolutionary equations.

Evolution Equations

Author : Gisele Ruiz Goldstein
Publisher : CRC Press
ISBN 13 : 9780824709754
Total Pages : 442 pages
Book Rating : 4.7/5 (97 download)

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Book Synopsis Evolution Equations by : Gisele Ruiz Goldstein

Download or read book Evolution Equations written by Gisele Ruiz Goldstein and published by CRC Press. This book was released on 2003-06-24 with total page 442 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 linear and nonlinear partial differential equations, and studies the latest theoretical developments and uses of evolution equations in a variety of disciplines. Providing nearly 500 references, the book contains discussions by renowned mathematicians such as H. Brezis, G. Da Prato, N.E. Gretskij, I. Lasiecka, Peter Lax, M. M. Rao, and R. Triggiani.

Geometric Evolution Equations

Author : Shu-Cheng Chang
Publisher : American Mathematical Soc.
ISBN 13 : 0821833618
Total Pages : 250 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Geometric Evolution Equations by : Shu-Cheng Chang

Download or read book Geometric Evolution Equations written by Shu-Cheng Chang and published by American Mathematical Soc.. This book was released on 2005 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Workshop on Geometric Evolution Equations was a gathering of experts that produced this comprehensive collection of articles. Many of the papers relate to the Ricci flow and Hamilton's program for understanding the geometry and topology of 3-manifolds. The use of evolution equations in geometry can lead to remarkable results. Of particular interest is the potential solution of Thurston's Geometrization Conjecture and the Poincare Conjecture. Yet applying the method poses serious technical problems. Contributors to this volume explain some of these issues and demonstrate a noteworthy deftness in the handling of technical areas. Various topics in geometric evolution equations and related fields are presented. Among other topics covered are minimal surface equations, mean curvature flow, harmonic map flow, Calabi flow, Ricci flow (including a numerical study), Kahler-Ricci flow, function theory on Kahler manifolds, flows of plane curves, convexity estimates, and the Christoffel-Minkowski problem. The material is suitable for graduate students and researchers interested in geometric analysis and connections to topology. Related titles of interest include The Ricci Flow: An Introduction.

Evolution Equations

Author : Kaïs Ammari
Publisher : Cambridge University Press
ISBN 13 : 1108329594
Total Pages : 205 pages
Book Rating : 4.1/5 (83 download)

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Book Synopsis Evolution Equations by : Kaïs Ammari

Download or read book Evolution Equations written by Kaïs Ammari and published by Cambridge University Press. This book was released on 2017-10-05 with total page 205 pages. Available in PDF, EPUB and Kindle. Book excerpt: The proceedings of the summer school held at the Université Savoie Mont Blanc, France, 'Mathematics in Savoie 2015', whose theme was long time behavior and control of evolution equations. The event was attended by world-leading researchers from the community of control theory, as well as young researchers from around the globe. This volume contains surveys of active research topics, along with original research papers containing exciting new results on the behavior of evolution equations. It will therefore benefit both graduate students and researchers. Key topics include the recent view on the controllability of parabolic systems that permits the reader to overview the moment method for parabolic equations, as well as numerical stabilization and control of partial differential equations.

Evolution Equations, Semigroups and Functional Analysis

Author : Alfredo Lorenzi
Publisher : Birkhäuser
ISBN 13 : 3034882211
Total Pages : 404 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis Evolution Equations, Semigroups and Functional Analysis by : Alfredo Lorenzi

Download or read book Evolution Equations, Semigroups and Functional Analysis written by Alfredo Lorenzi and published by Birkhäuser. This book was released on 2012-12-06 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.