Specific Asymptotic Properties Of The Solutions Of Impulsive Differential Equations Methods And Applications
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Nonlinear Higher Order Differential And Integral Coupled Systems: Impulsive And Integral Equations On Bounded And Unbounded Domains
| Author | : Feliz Manuel Minhos |
| Publisher | : World Scientific |
| Total Pages | : 243 |
| Release | : 2022-04-11 |
| Genre | : Mathematics |
| ISBN | : 9811225141 |
Boundary value problems on bounded or unbounded intervals, involving two or more coupled systems of nonlinear differential and integral equations with full nonlinearities, are scarce in the literature. The present work by the authors desires to fill this gap. The systems covered here include differential and integral equations of Hammerstein-type with boundary constraints, on bounded or unbounded intervals. These are presented in several forms and conditions (three points, mixed, with functional dependence, homoclinic and heteroclinic, amongst others). This would be the first time that differential and integral coupled systems are studied systematically. The existence, and in some cases, the localization of the solutions are carried out in Banach space, following several types of arguments and approaches such as Schauder's fixed-point theorem or Guo-Krasnosel'ski? fixed-point theorem in cones, allied to Green's function or its estimates, lower and upper solutions, convenient truncatures, the Nagumo condition presented in different forms, the concept of equiconvergence, Carathéodory functions, and sequences. Moreover, the final part in the volume features some techniques on how to relate differential coupled systems to integral ones, which require less regularity. Parallel to the theoretical explanation of this work, there is a range of practical examples and applications involving real phenomena, focusing on physics, mechanics, biology, forestry, and dynamical systems, which researchers and students will find useful.
Mathematical Modeling of Discontinuous Processes
| Author | : Andrey Antonov |
| Publisher | : Scientific Research Publishing, Inc. USA |
| Total Pages | : 239 |
| Release | : 2017-12-19 |
| Genre | : Mathematics |
| ISBN | : 1618964402 |
In this monograph as a mathematical apparatus are used and investigated several classes of differential equations. The most significant feature of these differential equations is the presence of impulsive effects. The main goals and the results achieved in the monograph are related to the use of this class of equation for an adequate description of the dynamics of several types of processes that are subject to discrete external interventions and change the speed of development. In all proposed models the following requirements have met: 1) Presented and studied mathematical models in the book are extensions of existing known in the literature models of real objects and related processes. 2) Generalizations of the studied models are related to the admission of external impulsive effects, which lead to “jump-like” change the quantity characteristics of the described object as well as the rate of its modification. 3) Sufficient conditions which guarantee certain qualities of the dynamics of the quantities of the modeled objects are found. 4) Studies of the qualities of the modification of the modeled objects are possible to be successful by differential equations with variable structure and impulsive effects. 5) The considerations relating to the existence of the studied properties of dynamic objects cannot be realized without introducing new concepts and proving of appropriate theorems. The main objectives can be conditionally divided into several parts: 1) New classes of differential equations with variable structure and impulses are introduced and studied; 2) Specific properties of the above-mentioned class of differential equations are introduced and studied. The present monograph consists of an introduction and seven chapters. Each chapter contains several sections.
Impulsive Differential Equations: Asymptotic Properties Of The Solutions
| Author | : Drumi D Bainov |
| Publisher | : World Scientific |
| Total Pages | : 246 |
| Release | : 1995-03-29 |
| Genre | : Mathematics |
| ISBN | : 9814501883 |
The question of the presence of various asymptotic properties of the solutions of ordinary differential equations arises when solving various practical problems. The investigation of these questions is still more important for impulsive differential equations which have a wider field of application than the ordinary ones.The results obtained by treating the asymptotic properties of the solutions of impulsive differential equations can be found in numerous separate articles. The systematized exposition of these results in a separate book will satisfy the growing interest in the problems related to the asymptotic properties of the solutions of impulsive differential equations and their applications.
Stability Analysis of Impulsive Functional Differential Equations
| Author | : Ivanka Stamova |
| Publisher | : Walter de Gruyter |
| Total Pages | : 241 |
| Release | : 2009 |
| Genre | : Mathematics |
| ISBN | : 3110221810 |
The aim of the Expositions is to present new and important developments in pure and applied mathematics. Well established in the community over more than two decades, the series offers a large library of mathematical works, including several important classics. The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers interested in a thorough study of the subject. Editorial Board Lev Birbrair, Universidade Federal do Cear , Fortaleza, Brasil Walter D. Neumann, Columbia University, New York, USA Markus J. Pflaum, University of Colorado, Boulder, USA Dierk Schleicher, Jacobs University, Bremen, Germany Katrin Wendland, University of Freiburg, Germany Honorary Editor Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia Titles in planning include Yuri A. Bahturin, Identical Relations in Lie Algebras (2019) Yakov G. Berkovich, Lev G. Kazarin, and Emmanuel M. Zhmud', Characters of Finite Groups, Volume 2 (2019) Jorge Herbert Soares de Lira, Variational Problems for Hypersurfaces in Riemannian Manifolds (2019) Volker Mayer, Mariusz Urbański, and Anna Zdunik, Random and Conformal Dynamical Systems (2021) Ioannis Diamantis, Bostjan Gabrovsek, Sofia Lambropoulou, and Maciej Mroczkowski, Knot Theory of Lens Spaces (2021)
Impulsive Differential Equations
| Author | : Dimit?r Ba?nov |
| Publisher | : World Scientific |
| Total Pages | : 246 |
| Release | : 1995 |
| Genre | : Mathematics |
| ISBN | : 9810218230 |
The question of the presence of various asymptotic properties of the solutions of ordinary differential equations arises when solving various practical problems. The investigation of these questions is still more important for impulsive differential equations which have a wider field of application than the ordinary ones.The results obtained by treating the asymptotic properties of the solutions of impulsive differential equations can be found in numerous separate articles. The systematized exposition of these results in a separate book will satisfy the growing interest in the problems related to the asymptotic properties of the solutions of impulsive differential equations and their applications.
Numerical Methods for Viscosity Solutions and Applications
| Author | : Maurizio Falcone |
| Publisher | : World Scientific |
| Total Pages | : 256 |
| Release | : 2001 |
| Genre | : Mathematics |
| ISBN | : 9789812799807 |
Geometrical optics and viscosity solutions / A.-P. Blanc, G. T. Kossioris and G. N. Makrakis -- Computation of vorticity evolution for a cylindrical Type-II superconductor subject to parallel and transverse applied magnetic fields / A. Briggs ... [et al.] -- A characterization of the value function for a class of degenerate control problems / F. Camilli -- Some microstructures in three dimensions / M. Chipot and V. Lecuyer -- Convergence of numerical schemes for the approximation of level set solutions to mean curvature flow / K. Deckelnick and G. Dziuk -- Optimal discretization steps in semi-lagrangian approximation of first-order PDEs / M. Falcone, R. Ferretti and T. Manfroni -- Convergence past singularities to the forced mean curvature flow for a modified reaction-diffusion approach / F. Fierro -- The viscosity-duality solutions approach to geometric pptics for the Helmholtz equation / L. Gosse and F. James -- Adaptive grid generation for evolutive Hamilton-Jacobi-Bellman equations / L. Grune -- Solution and application of anisotropic curvature driven evolution of curves (and surfaces) / K. Mikula -- An adaptive scheme on unstructured grids for the shape-from-shading problem / M. Sagona and A. Seghini -- On a posteriori error estimation for constant obstacle problems / A. Veeser.
Hyperbolic Functional Differential Inequalities and Applications
| Author | : Z. Kamont |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 318 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 9401146357 |
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.
Fractional Differential Equations, Inclusions and Inequalities with Applications
| Author | : Sotiris K. Ntouyas |
| Publisher | : MDPI |
| Total Pages | : 518 |
| Release | : 2020-11-09 |
| Genre | : Mathematics |
| ISBN | : 3039432184 |
During the last decade, there has been an increased interest in fractional differential equations, inclusions, and inequalities, as they play a fundamental role in the modeling of numerous phenomena, in particular, in physics, biomathematics, blood flow phenomena, ecology, environmental issues, viscoelasticity, aerodynamics, electrodynamics of complex medium, electrical circuits, electron-analytical chemistry, control theory, etc. This book presents collective works published in the recent Special Issue (SI) entitled "Fractional Differential Equation, Inclusions and Inequalities with Applications" of the journal Mathematics. This Special Issue presents recent developments in the theory of fractional differential equations and inequalities. Topics include but are not limited to the existence and uniqueness results for boundary value problems for different types of fractional differential equations, a variety of fractional inequalities, impulsive fractional differential equations, and applications in sciences and engineering.
Mathematical Methods In Electromagnetism: Linear Theory And Applications
| Author | : Michel Cessenat |
| Publisher | : World Scientific |
| Total Pages | : 396 |
| Release | : 1996-07-13 |
| Genre | : Mathematics |
| ISBN | : 9814525383 |
This book provides the reader with basic tools to solve problems of electromagnetism in their natural functional frameworks thanks to modern mathematical methods: integral surface methods, and also semigroups, variational methods, etc., well adapted to a numerical approach.As examples of applications of these tools and concepts, we solve several fundamental problems of electromagnetism, stationary or time-dependent: scattering of an incident wave by an obstacle, bounded or not, by gratings; wave propagation in a waveguide, with junctions and cascades. We hope that mathematical notions will allow a better understanding of modelization in electromagnetism and emphasize the essential features related to the geometry and nature of materials.
