Proceedings of the Conference on Differential & Difference Equations and Applications

Proceedings of the Conference on Differential & Difference Equations and Applications PDF Author: Ravi P. Agarwal
Publisher: Hindawi Publishing Corporation
ISBN: 9789775945389
Category : Difference equations
Languages : en
Pages : 1266

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Proceedings of the Conference on Differential & Difference Equations and Applications

Proceedings of the Conference on Differential & Difference Equations and Applications PDF Author: Ravi P. Agarwal
Publisher: Hindawi Publishing Corporation
ISBN: 9789775945389
Category : Difference equations
Languages : en
Pages : 1266

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Book Description


Hyperbolic Functional Differential Inequalities and Applications

Hyperbolic Functional Differential Inequalities and Applications PDF Author: Z. Kamont
Publisher: Springer Science & Business Media
ISBN: 9401146357
Category : Mathematics
Languages : en
Pages : 318

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Book Description
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.

Hyperbolic Partial Differential Equations

Hyperbolic Partial Differential Equations PDF Author: Serge Alinhac
Publisher: Springer Science & Business Media
ISBN: 0387878238
Category : Mathematics
Languages : en
Pages : 159

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Book Description
This excellent introduction to hyperbolic differential equations is devoted to linear equations and symmetric systems, as well as conservation laws. The book is divided into two parts. The first, which is intuitive and easy to visualize, includes all aspects of the theory involving vector fields and integral curves; the second describes the wave equation and its perturbations for two- or three-space dimensions. Over 100 exercises are included, as well as "do it yourself" instructions for the proofs of many theorems. Only an understanding of differential calculus is required. Notes at the end of the self-contained chapters, as well as references at the end of the book, enable ease-of-use for both the student and the independent researcher.

Mathematical Neuroscience

Mathematical Neuroscience PDF Author: Stanislaw Brzychczy
Publisher: Academic Press
ISBN: 0124104827
Category : Mathematics
Languages : en
Pages : 201

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Book Description
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

Functional Differential Equations

Functional Differential Equations PDF Author:
Publisher:
ISBN:
Category : Functional differential equations
Languages : en
Pages : 494

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Keller-Box Method and Its Application

Keller-Box Method and Its Application PDF Author: Kuppalapalle Vajravelu
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110271788
Category : Science
Languages : en
Pages : 414

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Book Description
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.

Topics in Fractional Differential Equations

Topics in Fractional Differential Equations PDF Author: Saïd Abbas
Publisher: Springer Science & Business Media
ISBN: 146144036X
Category : Mathematics
Languages : en
Pages : 403

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Book Description
​​​ Topics in Fractional Differential Equations is devoted to the existence and uniqueness of solutions for various classes of Darboux problems for hyperbolic differential equations or inclusions involving the Caputo fractional derivative. ​​Fractional calculus generalizes the integrals and derivatives to non-integer orders. During the last decade, fractional calculus was found to play a fundamental role in the modeling of a considerable number of phenomena; in particular the modeling of memory-dependent and complex media such as porous media. It has emerged as an important tool for the study of dynamical systems where classical methods reveal strong limitations. Some equations present delays which may be finite, infinite, or state-dependent. Others are subject to an impulsive effect. The above problems are studied using the fixed point approach, the method of upper and lower solution, and the Kuratowski measure of noncompactness. This book is addressed to a wide audience of specialists such as mathematicians, engineers, biologists, and physicists. ​

Impulsive Differential Equations and Inclusions

Impulsive Differential Equations and Inclusions PDF Author: Mouffak Benchohra
Publisher: Hindawi Publishing Corporation
ISBN: 977594550X
Category : Differential equations
Languages : en
Pages : 381

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Integration on Infinite-Dimensional Surfaces and Its Applications

Integration on Infinite-Dimensional Surfaces and Its Applications PDF Author: A. Uglanov
Publisher: Springer Science & Business Media
ISBN: 9401596220
Category : Mathematics
Languages : en
Pages : 280

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Book Description
It seems hard to believe, but mathematicians were not interested in integration problems on infinite-dimensional nonlinear structures up to 70s of our century. At least the author is not aware of any publication concerning this theme, although as early as 1967 L. Gross mentioned that the analysis on infinite dimensional manifolds is a field of research with rather rich opportunities in his classical work [2. This prediction was brilliantly confirmed afterwards, but we shall return to this later on. In those days the integration theory in infinite dimensional linear spaces was essentially developed in the heuristic works of RP. Feynman [1], I. M. Gelfand, A. M. Yaglom [1]). The articles of J. Eells [1], J. Eells and K. D. Elworthy [1], H. -H. Kuo [1], V. Goodman [1], where the contraction of a Gaussian measure on a hypersurface, in particular, was built and the divergence theorem (the Gauss-Ostrogradskii formula) was proved, appeared only in the beginning of the 70s. In this case a Gaussian specificity was essential and it was even pointed out in a later monograph of H. -H. Kuo [3] that the surface measure for the non-Gaussian case construction problem is not simple and has not yet been solved. A. V. Skorokhod [1] and the author [6,10] offered different approaches to such a construction. Some other approaches were offered later by Yu. L. Daletskii and B. D. Maryanin [1], O. G. Smolyanov [6], N. V.

Journal of analysis and its applications

Journal of analysis and its applications PDF Author:
Publisher:
ISBN:
Category : Mathematical analysis
Languages : en
Pages : 540

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