Abstract Parabolic Evolution Equations and their Applications - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Abstract Parabolic Evolution Equations and their Applications write by Atsushi Yagi. This book was released on 2009-11-03. Abstract Parabolic Evolution Equations and their Applications available in PDF, EPUB and Kindle. 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
Surface Evolution Equations - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Surface Evolution Equations write by Yoshikazu Giga. This book was released on 2006-03-30. Surface Evolution Equations available in PDF, EPUB and Kindle. 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
Evolution Equations and Approximations - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Evolution Equations and Approximations write by Kazufumi Ito. This book was released on 2002. Evolution Equations and Approximations available in PDF, EPUB and Kindle. 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
Semigroup Methods for Evolution Equations on Networks - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Semigroup Methods for Evolution Equations on Networks write by Delio Mugnolo. This book was released on 2014-05-21. Semigroup Methods for Evolution Equations on Networks available in PDF, EPUB and Kindle. 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.
Nonlinear Evolution Equations - Global Behavior of Solutions
Nonlinear Evolution Equations - Global Behavior of Solutions - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Nonlinear Evolution Equations - Global Behavior of Solutions write by Alain Haraux. This book was released on 2006-11-15. Nonlinear Evolution Equations - Global Behavior of Solutions available in PDF, EPUB and Kindle.
