Hyperbolic Functional Differential Inequalities And Applications
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Hyperbolic Functional Differential Inequalities And Applications
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Author : Z. Kamont
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Hyperbolic Functional Differential Inequalities And Applications written by Z. Kamont and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
This book is intended as a self-contained exposition of hyperbolic functional dif ferential inequalities and their applications. Its aim is to give a systematic and unified presentation of recent developments of the following problems: (i) functional differential inequalities generated by initial and mixed problems, (ii) existence theory of local and global solutions, (iii) functional integral equations generated by hyperbolic equations, (iv) numerical method of lines for hyperbolic problems, (v) difference methods for initial and initial-boundary value problems. Beside classical solutions, the following classes of weak solutions are treated: Ca ratheodory solutions for quasilinear equations, entropy solutions and viscosity so lutions for nonlinear problems and solutions in the Friedrichs sense for almost linear equations. The theory of difference and differential difference equations ge nerated by original problems is discussed and its applications to the constructions of numerical methods for functional differential problems are presented. The monograph is intended for different groups of scientists. Pure mathemati cians and graduate students will find an advanced theory of functional differential problems. Applied mathematicians and research engineers will find numerical al gorithms for many hyperbolic problems. The classical theory of partial differential inequalities has been described exten sively in the monographs [138, 140, 195, 225). As is well known, they found applica tions in differential problems. The basic examples of such questions are: estimates of solutions of partial equations, estimates of the domain of the existence of solu tions, criteria of uniqueness and estimates of the error of approximate solutions.
Differential And Integral Inequalities Theory And Applications Part B Functional Partial Abstract And Complex Differential Equations
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Author : Lakshmikantham
language : en
Publisher: Academic Press
Release Date : 1969
Differential And Integral Inequalities Theory And Applications Part B Functional Partial Abstract And Complex Differential Equations written by Lakshmikantham and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1969 with Computers categories.
Differential and integral inequalities; theory and applications PART B: Functional, partial, abstract, and complex differential equations
Differential And Integral Inequalities Theory And Applications
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Author : V. Lakshmikantham
language : en
Publisher: Academic Press
Release Date : 1969
Differential And Integral Inequalities Theory And Applications written by V. Lakshmikantham and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1969 with Computers categories.
This volume constitutes the first part of a monograph on theory and applications of differential and integral inequalities. 'The entire work, as a whole, is intended to be a research monograph, a guide to the literature, and a textbook for advanced courses. The unifying theme of this treatment is a systematic development of the theory and applications of differential inequalities as well as Volterra integral inequalities. The main tools for applications are the norm and the Lyapunov functions. Familiarity with real and complex analysis, elements of general topology and functional analysis, and differential and integral equations is assumed.
Differential And Integral Inequalities Functional Partial Abstract And Complex Differential Equations
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Author : V. Lakshmikantham
language : en
Publisher:
Release Date : 1969
Differential And Integral Inequalities Functional Partial Abstract And Complex Differential Equations written by V. Lakshmikantham and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1969 with Differential equations categories.
Differential And Integral Inequalities
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Author : Wolfgang Walter
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Differential And Integral Inequalities written by Wolfgang Walter and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
In 1964 the author's mono graph "Differential- und Integral-Un gleichungen," with the subtitle "und ihre Anwendung bei Abschätzungs und Eindeutigkeitsproblemen" was published. The present volume grew out of the response to the demand for an English translation of this book. In the meantime the literature on differential and integral in equalities increased greatly. We have tried to incorporate new results as far as possible. As a matter of fact, the Bibliography has been almost doubled in size. The most substantial additions are in the field of existence theory. In Chapter I we have included the basic theorems on Volterra integral equations in Banach space (covering the case of ordinary differential equations in Banach space). Corresponding theorems on differential inequalities have been added in Chapter II. This was done with a view to the new sections; dealing with the line method, in the chapter on parabolic differential equations. Section 35 contains an exposition of this method in connection with estimation and convergence. An existence theory for the general nonlinear parabolic equation in one space variable based on the line method is given in Section 36. This theory is considered by the author as one of the most significant recent applications of in equality methods. We should mention that an exposition of Krzyzanski's method for solving the Cauchy problem has also been added. The numerous requests that the new edition include a chapter on elliptic differential equations have been satisfied to some extent.
Mathematical Neuroscience
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Author : Stanislaw Brzychczy
language : en
Publisher: Academic Press
Release Date : 2013-08-16
Mathematical Neuroscience written by Stanislaw Brzychczy and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-08-16 with Mathematics categories.
Mathematical Neuroscience is a book for mathematical biologists seeking to discover the complexities of brain dynamics in an integrative way. It is the first research monograph devoted exclusively to the theory and methods of nonlinear analysis of infinite systems based on functional analysis techniques arising in modern mathematics. Neural models that describe the spatio-temporal evolution of coarse-grained variables—such as synaptic or firing rate activity in populations of neurons —and often take the form of integro-differential equations would not normally reflect an integrative approach. This book examines the solvability of infinite systems of reaction diffusion type equations in partially ordered abstract spaces. It considers various methods and techniques of nonlinear analysis, including comparison theorems, monotone iterative techniques, a truncation method, and topological fixed point methods. Infinite systems of such equations play a crucial role in the integrative aspects of neuroscience modeling. The first focused introduction to the use of nonlinear analysis with an infinite dimensional approach to theoretical neuroscience Combines functional analysis techniques with nonlinear dynamical systems applied to the study of the brain Introduces powerful mathematical techniques to manage the dynamics and challenges of infinite systems of equations applied to neuroscience modeling
The Darboux Problem For Hyperbolic Functional Differential Equations And Inequalities In The Sense Of Carath Odory
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Author : Adrian Karpowicz
language : en
Publisher:
Release Date : 2010
The Darboux Problem For Hyperbolic Functional Differential Equations And Inequalities In The Sense Of Carath Odory written by Adrian Karpowicz and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with categories.
Multi Dimensional Hyperbolic Partial Differential Equations
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Author : Sylvie Benzoni-Gavage
language : en
Publisher: Oxford University Press, USA
Release Date : 2007
Multi Dimensional Hyperbolic Partial Differential Equations written by Sylvie Benzoni-Gavage and has been published by Oxford University Press, USA this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.
Authored by leading scholars, this comprehensive text presents a view of the multi-dimensional hyperbolic partial differential equations, with a particular emphasis on problems in which modern tools of analysis have proved useful. It is useful to graduates and researchers in both hyperbolic PDEs and compressible fluid dynamics.
Hyperbolic Partial Differential Equations
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Author : Peter D. Lax
language : en
Publisher: American Mathematical Soc.
Release Date : 2006
Hyperbolic Partial Differential Equations written by Peter D. Lax and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Differential equations, Hyperbolic categories.
The theory of hyperbolic equations is a large subject, and its applications are many: fluid dynamics and aerodynamics, the theory of elasticity, optics, electromagnetic waves, direct and inverse scattering, and the general theory of relativity. This book is an introduction to most facets of the theory and is an ideal text for a second-year graduate course on the subject. The first part deals with the basic theory: the relation of hyperbolicity to the finite propagation of signals, the concept and role of characteristic surfaces and rays, energy, and energy inequalities. The structure of solutions of equations with constant coefficients is explored with the help of the Fourier and Radon transforms. The existence of solutions of equations with variable coefficients with prescribed initial values is proved using energy inequalities. The propagation of singularities is studied with the help of progressing waves. The second part describes finite difference approximations of hyperbolic equations, presents a streamlined version of the Lax-Phillips scattering theory, and covers basic concepts and results for hyperbolic systems of conservation laws, an active research area today. Four brief appendices sketch topics that are important or amusing, such as Huygens' principle and a theory of mixed initial and boundary value problems. A fifth appendix by Cathleen Morawetz describes a nonstandard energy identity and its uses. Information for our distributors: Titles in this series are copublished with the Courant Institute of Mathematical Sciences at New York University.
Keller Box Method And Its Application
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Author : Kuppalapalle Vajravelu
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2014-06-18
Keller Box Method And Its Application written by Kuppalapalle Vajravelu and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-06-18 with Science categories.
Most of the problems arising in science and engineering are nonlinear. They are inherently difficult to solve. Traditional analytical approximations are valid only for weakly nonlinear problems, and often break down for problems with strong nonlinearity. This book presents the current theoretical developments and applications of the Keller-box method to nonlinear problems. The first half of the book addresses basic concepts to understand the theoretical framework for the method. In the second half of the book, the authors give a number of examples of coupled nonlinear problems that have been solved by means of the Keller-box method. The particular area of focus is on fluid flow problems governed by nonlinear equation.