Semilinear Evolution Equations And Their Applications

Author : Toka Diagana
Publisher : Springer
Page : 189 pages
File Size : 49,7 Mb
Release : 2018-10-23
Category : Mathematics
ISBN : 9783030004491

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Semilinear Evolution Equations and Their Applications by Toka Diagana Pdf

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.

Author : Thierry Cazenave,Alain Haraux
Publisher : Oxford University Press
Page : 204 pages
File Size : 44,8 Mb
Release : 1998
Category : Computers
ISBN : 019850277X

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An Introduction to Semilinear Evolution Equations by Thierry Cazenave,Alain Haraux Pdf

This book presents in a self-contained form the typical basic properties of solutions to semilinear evolutionary partial differential equations, with special emphasis on global properties. It has a didactic ambition and will be useful for an applied readership as well as theoretical researchers.

Author : Thierry Cazenave
Publisher : Unknown
Page : 186 pages
File Size : 50,6 Mb
Release : 2006
Category : Electronic
ISBN : OCLC:1082072617

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An Introduction to Semilinear Evolution Equations by Thierry Cazenave Pdf

Author : Atsushi Yagi
Publisher : Springer Science & Business Media
Page : 594 pages
File Size : 43,6 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 : Kazufumi Ito,F. Kappel
Publisher : World Scientific
Page : 524 pages
File Size : 55,9 Mb
Release : 2002
Category : Science
ISBN : 9812380264

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Evolution Equations and Approximations by Kazufumi Ito,F. Kappel Pdf

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

Author : D Daners,P Koch-Medina
Publisher : Chapman and Hall/CRC
Page : 268 pages
File Size : 40,8 Mb
Release : 1992-12-29
Category : Mathematics
ISBN : UOM:39015049316576

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Abstract Evolution Equations, Periodic Problems and Applications by D Daners,P Koch-Medina Pdf

Part of the Pitman Research Notes in Mathematics series, this text covers: linear evolution equations of parabolic type; semilinear evolution equations of parabolic type; evolution equations and positivity; semilinear periodic evolution equations; and applications.

Author : Mimmo Iannelli,Gunter Lumer
Publisher : Birkhäuser
Page : 419 pages
File Size : 49,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034880855

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Evolution Equations: Applications to Physics, Industry, Life Sciences and Economics by Mimmo Iannelli,Gunter Lumer Pdf

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 : G Lumer
Publisher : CRC Press
Page : 532 pages
File Size : 46,6 Mb
Release : 2019-04-24
Category : Medical
ISBN : 9781482277487

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Evolution Equations and Their Applications in Physical and Life Sciences by G Lumer Pdf

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 : Belleni-morante Aldo
Publisher : World Scientific
Page : 180 pages
File Size : 46,9 Mb
Release : 1994-05-18
Category : Mathematics
ISBN : 9789813104570

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A Concise Guide To Semigroups And Evolution Equations by Belleni-morante Aldo Pdf

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 : Bei Hu
Publisher : Springer Science & Business Media
Page : 137 pages
File Size : 44,5 Mb
Release : 2011-03-23
Category : Mathematics
ISBN : 9783642184598

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Blow-up Theories for Semilinear Parabolic Equations by Bei Hu Pdf

There is an enormous amount of work in the literature about the blow-up behavior of evolution equations. It is our intention to introduce the theory by emphasizing the methods while seeking to avoid massive technical computations. To reach this goal, we use the simplest equation to illustrate the methods; these methods very often apply to more general equations.

Author : A.V. Babin,M.I. Vishik
Publisher : Elsevier
Page : 543 pages
File Size : 48,7 Mb
Release : 1992-03-09
Category : Mathematics
ISBN : 9780080875460

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Attractors of Evolution Equations by A.V. Babin,M.I. Vishik Pdf

Problems, ideas and notions from the theory of finite-dimensional dynamical systems have penetrated deeply into the theory of infinite-dimensional systems and partial differential equations. From the standpoint of the theory of the dynamical systems, many scientists have investigated the evolutionary equations of mathematical physics. Such equations include the Navier-Stokes system, magneto-hydrodynamics equations, reaction-diffusion equations, and damped semilinear wave equations. Due to the recent efforts of many mathematicians, it has been established that the attractor of the Navier-Stokes system, which attracts (in an appropriate functional space) as t - ∞ all trajectories of this system, is a compact finite-dimensional (in the sense of Hausdorff) set. Upper and lower bounds (in terms of the Reynolds number) for the dimension of the attractor were found. These results for the Navier-Stokes system have stimulated investigations of attractors of other equations of mathematical physics. For certain problems, in particular for reaction-diffusion systems and nonlinear damped wave equations, mathematicians have established the existence of the attractors and their basic properties; furthermore, they proved that, as t - +∞, an infinite-dimensional dynamics described by these equations and systems uniformly approaches a finite-dimensional dynamics on the attractor U, which, in the case being considered, is the union of smooth manifolds. This book is devoted to these and several other topics related to the behaviour as t - ∞ of solutions for evolutionary equations.

Author : Mark McKibben
Publisher : Chapman and Hall/CRC
Page : 0 pages
File Size : 46,8 Mb
Release : 2011-06-03
Category : Mathematics
ISBN : 1420092111

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Discovering Evolution Equations with Applications by Mark McKibben Pdf

Most existing books on evolution equations tend either to cover a particular class of equations in too much depth for beginners or focus on a very specific research direction. Thus, the field can be daunting for newcomers to the field who need access to preliminary material and behind-the-scenes detail. Taking an applications-oriented, conversational approach, Discovering Evolution Equations with Applications: Volume 2-Stochastic Equations provides an introductory understanding of stochastic evolution equations. The text begins with hands-on introductions to the essentials of real and stochastic analysis. It then develops the theory for homogenous one-dimensional stochastic ordinary differential equations (ODEs) and extends the theory to systems of homogenous linear stochastic ODEs. The next several chapters focus on abstract homogenous linear, nonhomogenous linear, and semi-linear stochastic evolution equations. The author also addresses the case in which the forcing term is a functional before explaining Sobolev-type stochastic evolution equations. The last chapter discusses several topics of active research. Each chapter starts with examples of various models. The author points out the similarities of the models, develops the theory involved, and then revisits the examples to reinforce the theoretical ideas in a concrete setting. He incorporates a substantial collection of questions and exercises throughout the text and provides two layers of hints for selected exercises at the end of each chapter. Suitable for readers unfamiliar with analysis even at the undergraduate level, this book offers an engaging and accessible account of core theoretical results of stochastic evolution equations in a way that gradually builds readers’ intuition.

Author : Mark McKibben
Publisher : CRC Press
Page : 456 pages
File Size : 44,8 Mb
Release : 2011-06-03
Category : Mathematics
ISBN : 9781420092127

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Discovering Evolution Equations with Applications by Mark McKibben Pdf

Most existing books on evolution equations tend either to cover a particular class of equations in too much depth for beginners or focus on a very specific research direction. Thus, the field can be daunting for newcomers to the field who need access to preliminary material and behind-the-scenes detail. Taking an applications-oriented, conversation

Author : Solym Mawaki Manou-Abi,Sophie Dabo-Niang,Jean-Jacques Salone
Publisher : John Wiley & Sons
Page : 308 pages
File Size : 52,5 Mb
Release : 2020-04-28
Category : Mathematics
ISBN : 9781786304544

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Mathematical Modeling of Random and Deterministic Phenomena by Solym Mawaki Manou-Abi,Sophie Dabo-Niang,Jean-Jacques Salone Pdf

This book highlights mathematical research interests that appear in real life, such as the study and modeling of random and deterministic phenomena. As such, it provides current research in mathematics, with applications in biological and environmental sciences, ecology, epidemiology and social perspectives. The chapters can be read independently of each other, with dedicated references specific to each chapter. The book is organized in two main parts. The first is devoted to some advanced mathematical problems regarding epidemic models; predictions of biomass; space-time modeling of extreme rainfall; modeling with the piecewise deterministic Markov process; optimal control problems; evolution equations in a periodic environment; and the analysis of the heat equation. The second is devoted to a modelization with interdisciplinarity in ecological, socio-economic, epistemological, demographic and social problems. Mathematical Modeling of Random and Deterministic Phenomena is aimed at expert readers, young researchers, plus graduate and advanced undergraduate students who are interested in probability, statistics, modeling and mathematical analysis.

Author : Mihaela Manole
Publisher : LAP Lambert Academic Publishing
Page : 124 pages
File Size : 53,9 Mb
Release : 2012
Category : Electronic
ISBN : 3659295248

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Fixed Point Methods for the Study of Semilinear Evolution Equations by Mihaela Manole Pdf

Partial differential equations is a many-faceted subject. Created to describe the mechanical behavior of objects such as vibrating strings and blowing winds, it has developed into a body of material that interacts with many branches of mathematics, such as differential geometry, complex analysis, and harmonic analysis, as well as a ubiquitous factor in the description and elucidation of problems in mathematical physics. The goal of this work is to make more precise the operator approach for some evolution partial differential equations and extend the theory to semilinear operator systems. More exactly, we shall precise basic properties, such as norm estimation and compactness, for the (linear)solution operator associated to the non-homogeneous linear evolution equations and we shall use them in order to apply the Banach, Schauder and Leray-Schauder theorems to the fixed point problems equivalent to Chaichy-Dirichlet problems for evolution equations. We extend these results to the corresponding semilinear operator system.