Fixed Point Methods For The Study Of Semilinear Evolution Equations
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Fixed Point Methods for the Study of Semilinear Evolution Equations
Author | : Mihaela Manole |
Publisher | : LAP Lambert Academic Publishing |
Total Pages | : 124 |
Release | : 2012 |
Genre | : |
ISBN | : 9783659295249 |
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.
Semilinear Evolution Equations and Their Applications
Author | : Toka Diagana |
Publisher | : Springer |
Total Pages | : 199 |
Release | : 2018-10-23 |
Genre | : Mathematics |
ISBN | : 303000449X |
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.
An Introduction to Semilinear Evolution Equations
Author | : Thierry Cazenave |
Publisher | : Oxford University Press |
Total Pages | : 204 |
Release | : 1998 |
Genre | : Computers |
ISBN | : 9780198502777 |
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.
Abstract Evolution Equations, Periodic Problems and Applications
Author | : D Daners |
Publisher | : Chapman and Hall/CRC |
Total Pages | : 268 |
Release | : 1992-12-29 |
Genre | : Mathematics |
ISBN | : |
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.
Fixed Point Theorems and Applications
Author | : Vittorino Pata |
Publisher | : Springer Nature |
Total Pages | : 171 |
Release | : 2019-09-22 |
Genre | : Mathematics |
ISBN | : 3030196704 |
This book addresses fixed point theory, a fascinating and far-reaching field with applications in several areas of mathematics. The content is divided into two main parts. The first, which is more theoretical, develops the main abstract theorems on the existence and uniqueness of fixed points of maps. In turn, the second part focuses on applications, covering a large variety of significant results ranging from ordinary differential equations in Banach spaces, to partial differential equations, operator theory, functional analysis, measure theory, and game theory. A final section containing 50 problems, many of which include helpful hints, rounds out the coverage. Intended for Master’s and PhD students in Mathematics or, more generally, mathematically oriented subjects, the book is designed to be largely self-contained, although some mathematical background is needed: readers should be familiar with measure theory, Banach and Hilbert spaces, locally convex topological vector spaces and, in general, with linear functional analysis.
A Concise Guide To Semigroups And Evolution Equations
Author | : Aldo Belleni-morante |
Publisher | : World Scientific |
Total Pages | : 186 |
Release | : 1994-05-18 |
Genre | : Mathematics |
ISBN | : 9813104570 |
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).
Functional Analytic Methods for Evolution Equations
Author | : Giuseppe Da Prato |
Publisher | : Springer Science & Business Media |
Total Pages | : 486 |
Release | : 2004-09-22 |
Genre | : Mathematics |
ISBN | : 9783540230304 |
This book consists of five introductory contributions by leading mathematicians on the functional analytic treatment of evolutions equations. In particular the contributions deal with Markov semigroups, maximal L^p-regularity, optimal control problems for boundary and point control systems, parabolic moving boundary problems and parabolic nonautonomous evolution equations. The book is addressed to PhD students, young researchers and mathematicians doing research in one of the above topics.
Fractional Evolution Equations and Inclusions
Author | : Yong Zhou |
Publisher | : Academic Press |
Total Pages | : 296 |
Release | : 2016-02-05 |
Genre | : Mathematics |
ISBN | : 0128047755 |
Fractional evolution inclusions are an important form of differential inclusions within nonlinear mathematical analysis. They are generalizations of the much more widely developed fractional evolution equations (such as time-fractional diffusion equations) seen through the lens of multivariate analysis. Compared to fractional evolution equations, research on the theory of fractional differential inclusions is however only in its initial stage of development. This is important because differential models with the fractional derivative providing an excellent instrument for the description of memory and hereditary properties, and have recently been proved valuable tools in the modeling of many physical phenomena. The fractional order models of real systems are always more adequate than the classical integer order models, since the description of some systems is more accurate when the fractional derivative is used. The advantages of fractional derivatization become evident in modeling mechanical and electrical properties of real materials, description of rheological properties of rocks and in various other fields. Such models are interesting for engineers and physicists as well as so-called pure mathematicians. Phenomena investigated in hybrid systems with dry friction, processes of controlled heat transfer, obstacle problems and others can be described with the help of various differential inclusions, both linear and nonlinear. Fractional Evolution Equations and Inclusions is devoted to a rapidly developing area of the research for fractional evolution equations & inclusions and their applications to control theory. It studies Cauchy problems for fractional evolution equations, and fractional evolution inclusions with Hille-Yosida operators. It discusses control problems for systems governed by fractional evolution equations. Finally it provides an investigation of fractional stochastic evolution inclusions in Hilbert spaces. Systematic analysis of existence theory and topological structure of solution sets for fractional evolution inclusions and control systems Differential models with fractional derivative provide an excellent instrument for the description of memory and hereditary properties, and their description and working will provide valuable insights into the modelling of many physical phenomena suitable for engineers and physicists The book provides the necessary background material required to go further into the subject and explore the rich research literature
Evolution Equations
Author | : Aleksandr Andreevich Pankov |
Publisher | : |
Total Pages | : 340 |
Release | : 2018 |
Genre | : MATHEMATICS |
ISBN | : 9781536142594 |
This volume of Advances in Evolution Equations is dedicated to the memory of Professor Vasilii Vasilievich Zhikov, an outstanding Russian mathematician. Zhikov's scientific interest ranged from almost periodic differential equations and topological dynamics to spectral theory of elliptic operators, qualitative theory of parabolic equations, calculus of variations, homogenization, and hydrodynamics, to name a few. Many of his results are now classical.