Evolutionary Equations

Author : Christian Seifert
Publisher : Springer Nature
Page : 321 pages
File Size : 44,7 Mb
Release : 2022
Category : Differential equations
ISBN : 9783030893972

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Evolutionary Equations by Christian Seifert Pdf

This open access book provides a solution theory for time-dependent partial differential equations, which classically have not been accessible by a unified method. Instead of using sophisticated techniques and methods, the approach is elementary in the sense that only Hilbert space methods and some basic theory of complex analysis are required. Nevertheless, key properties of solutions can be recovered in an elegant manner. Moreover, the strength of this method is demonstrated by a large variety of examples, showing the applicability of the approach of evolutionary equations in various fields. Additionally, a quantitative theory for evolutionary equations is developed. The text is self-contained, providing an excellent source for a first study on evolutionary equations and a decent guide to the available literature on this subject, thus bridging the gap to state-of-the-art mathematical research.

Author : Jacek Banasiak,Mustapha Mokhtar-Kharroubi
Publisher : Springer
Page : 493 pages
File Size : 40,9 Mb
Release : 2014-11-07
Category : Mathematics
ISBN : 9783319113227

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Evolutionary Equations with Applications in Natural Sciences by Jacek Banasiak,Mustapha Mokhtar-Kharroubi Pdf

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.

Author : George R. Sell,Yuncheng You
Publisher : Springer Science & Business Media
Page : 680 pages
File Size : 53,7 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9781475750379

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Dynamics of Evolutionary Equations by George R. Sell,Yuncheng You Pdf

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.

Author : Martin A. Nowak
Publisher : Harvard University Press
Page : 390 pages
File Size : 47,9 Mb
Release : 2006-09-29
Category : Science
ISBN : 9780674417755

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Evolutionary Dynamics by Martin A. Nowak Pdf

At a time of unprecedented expansion in the life sciences, evolution is the one theory that transcends all of biology. Any observation of a living system must ultimately be interpreted in the context of its evolution. Evolutionary change is the consequence of mutation and natural selection, which are two concepts that can be described by mathematical equations. Evolutionary Dynamics is concerned with these equations of life. In this book, Martin A. Nowak draws on the languages of biology and mathematics to outline the mathematical principles according to which life evolves. His work introduces readers to the powerful yet simple laws that govern the evolution of living systems, no matter how complicated they might seem. Evolution has become a mathematical theory, Nowak suggests, and any idea of an evolutionary process or mechanism should be studied in the context of the mathematical equations of evolutionary dynamics. His book presents a range of analytical tools that can be used to this end: fitness landscapes, mutation matrices, genomic sequence space, random drift, quasispecies, replicators, the Prisoner’s Dilemma, games in finite and infinite populations, evolutionary graph theory, games on grids, evolutionary kaleidoscopes, fractals, and spatial chaos. Nowak then shows how evolutionary dynamics applies to critical real-world problems, including the progression of viral diseases such as AIDS, the virulence of infectious agents, the unpredictable mutations that lead to cancer, the evolution of altruism, and even the evolution of human language. His book makes a clear and compelling case for understanding every living system—and everything that arises as a consequence of living systems—in terms of evolutionary dynamics.

Author : Yoshikazu Giga
Publisher : Springer Science & Business Media
Page : 264 pages
File Size : 55,5 Mb
Release : 2006-03-30
Category : Mathematics
ISBN : 9783764373917

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Surface Evolution Equations by Yoshikazu Giga Pdf

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.

Author : C.M. Dafermos,Milan Pokorny
Publisher : Elsevier
Page : 609 pages
File Size : 42,5 Mb
Release : 2008-10-06
Category : Mathematics
ISBN : 9780080931975

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Handbook of Differential Equations: Evolutionary Equations by C.M. Dafermos,Milan Pokorny Pdf

The material collected in this volume discusses the present as well as expected future directions of development of the field with particular emphasis on applications. The seven survey articles present different topics in Evolutionary PDE’s, written by leading experts. - Review of new results in the area- Continuation of previous volumes in the handbook series covering Evolutionary PDEs- Written by leading experts

Author : Atsushi Yagi
Publisher : Springer Science & Business Media
Page : 594 pages
File Size : 53,8 Mb
Release : 2009-11-03
Category : Mathematics
ISBN : 9783642046315

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Abstract Parabolic Evolution Equations and their Applications by Atsushi Yagi Pdf

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

Author : Gisele Ruiz Goldstein,Rainer Nagel,Silvia Romanelli
Publisher : CRC Press
Page : 267 pages
File Size : 51,8 Mb
Release : 2019-04-24
Category : Mathematics
ISBN : 9780429530050

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Evolution Equations by Gisele Ruiz Goldstein,Rainer Nagel,Silvia Romanelli Pdf

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 : John A. Walker
Publisher : Springer Science & Business Media
Page : 244 pages
File Size : 45,7 Mb
Release : 2013-03-09
Category : Computers
ISBN : 9781468410365

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Dynamical Systems and Evolution Equations by John A. Walker Pdf

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.

Author : Alfredo Lorenzi,Bernhard Ruf
Publisher : Birkhäuser
Page : 404 pages
File Size : 52,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034882217

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Evolution Equations, Semigroups and Functional Analysis by Alfredo Lorenzi,Bernhard Ruf Pdf

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 : M. I. Vishik
Publisher : Cambridge University Press
Page : 172 pages
File Size : 42,7 Mb
Release : 1992
Category : Mathematics
ISBN : 052142237X

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Asymptotic Behaviour of Solutions of Evolutionary Equations by M. I. Vishik Pdf

A short but sweet summary of globally asymptotic solutions of evolutionary equations.

Author : Alain Haraux
Publisher : Springer
Page : 324 pages
File Size : 40,6 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540385349

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Nonlinear Evolution Equations - Global Behavior of Solutions by Alain Haraux Pdf

Author : Jan Prüss,Gieri Simonett
Publisher : Birkhäuser
Page : 609 pages
File Size : 49,7 Mb
Release : 2016-07-25
Category : Mathematics
ISBN : 9783319276984

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Moving Interfaces and Quasilinear Parabolic Evolution Equations by Jan Prüss,Gieri Simonett Pdf

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.

Author : Reinhard Racke,Song Jiang
Publisher : CRC Press
Page : 322 pages
File Size : 47,5 Mb
Release : 2000-06-21
Category : Mathematics
ISBN : 1584882158

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Evolution Equations in Thermoelasticity by Reinhard Racke,Song Jiang Pdf

Although the study of classical thermoelasticity has provided information on linear systems, only recently have results on the asymptotic behavior completed our basic understanding of the generic behavior of solutions. Through systematic work that began in the 80s, we now also understand the basic features of nonlinear systems. Yet some questions remain open, and the field has lacked a comprehensive survey that explores these past results and presents recent developments. Evolution Equations in Thermoelasticity presents a modern treatment of initial value problems and of initial boundary value problems in both linear and nonlinear thermoelasticity, in one- and multi-dimensional spatial configurations. The authors provide the first self-contained presentation of the subject that offers both introductory parts accessible to graduate students and sophisticated sections valuable to experts.

Author : Kenji Nakanishi,Wilhelm Schlag
Publisher : European Mathematical Society
Page : 264 pages
File Size : 46,6 Mb
Release : 2011
Category : Hamiltonian systems
ISBN : 3037190957

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Invariant Manifolds and Dispersive Hamiltonian Evolution Equations by Kenji Nakanishi,Wilhelm Schlag Pdf

The notion of an invariant manifold arises naturally in the asymptotic stability analysis of stationary or standing wave solutions of unstable dispersive Hamiltonian evolution equations such as the focusing semilinear Klein-Gordon and Schrodinger equations. This is due to the fact that the linearized operators about such special solutions typically exhibit negative eigenvalues (a single one for the ground state), which lead to exponential instability of the linearized flow and allows for ideas from hyperbolic dynamics to enter. One of the main results proved here for energy subcritical equations is that the center-stable manifold associated with the ground state appears as a hyper-surface which separates a region of finite-time blowup in forward time from one which exhibits global existence and scattering to zero in forward time. The authors' entire analysis takes place in the energy topology, and the conserved energy can exceed the ground state energy only by a small amount. This monograph is based on recent research by the authors. The proofs rely on an interplay between the variational structure of the ground states and the nonlinear hyperbolic dynamics near these states. A key element in the proof is a virial-type argument excluding almost homoclinic orbits originating near the ground states, and returning to them, possibly after a long excursion. These lectures are suitable for graduate students and researchers in partial differential equations and mathematical physics. For the cubic Klein-Gordon equation in three dimensions all details are provided, including the derivation of Strichartz estimates for the free equation and the concentration-compactness argument leading to scattering due to Kenig and Merle.