Viability Invariance and Applications

Viability  Invariance and Applications
Author: Ovidiu Carja,Mihai Necula,Ioan I. Vrabie
Publsiher: Elsevier
Total Pages: 356
Release: 2007-07-18
Genre: Mathematics
ISBN: 0080521665

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The book is an almost self-contained presentation of the most important concepts and results in viability and invariance. The viability of a set K with respect to a given function (or multi-function) F, defined on it, describes the property that, for each initial data in K, the differential equation (or inclusion) driven by that function or multi-function) to have at least one solution. The invariance of a set K with respect to a function (or multi-function) F, defined on a larger set D, is that property which says that each solution of the differential equation (or inclusion) driven by F and issuing in K remains in K, at least for a short time. The book includes the most important necessary and sufficient conditions for viability starting with Nagumo’s Viability Theorem for ordinary differential equations with continuous right-hand sides and continuing with the corresponding extensions either to differential inclusions or to semilinear or even fully nonlinear evolution equations, systems and inclusions. In the latter (i.e. multi-valued) cases, the results (based on two completely new tangency concepts), all due to the authors, are original and extend significantly, in several directions, their well-known classical counterparts. New concepts for multi-functions as the classical tangent vectors for functions Provides the very general and necessary conditions for viability in the case of differential inclusions, semilinear and fully nonlinear evolution inclusions Clarifying examples, illustrations and numerous problems, completely and carefully solved Illustrates the applications from theory into practice Very clear and elegant style

Differential Equations

Differential Equations
Author: Ioan I Vrabie
Publsiher: World Scientific Publishing Company
Total Pages: 480
Release: 2011-05-26
Genre: Mathematics
ISBN: 9789813108080

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This book presents, in a unitary frame and from a new perspective, the main concepts and results of one of the most fascinating branches of modern mathematics, namely differential equations, and offers the reader another point of view concerning a possible way to approach the problems of existence, uniqueness, approximation, and continuation of the solutions to a Cauchy problem. In addition, it contains simple introductions to some topics which are not usually included in classical textbooks: the exponential formula, conservation laws, generalized solutions, Caratheodory solutions, differential inclusions, variational inequalities, viability, invariance, gradient systems. In this new edition we have corrected several small errors and added the following new topics: Volterra Integral Equations and Elements of Calculus of Variations. Some problems and exercises, referring to these two new topics are also included. The bibliography has been updated and expanded.

Differential Equations

Differential Equations
Author: Ioan I Vrabie
Publsiher: World Scientific Publishing Company
Total Pages: 528
Release: 2016-05-30
Genre: Mathematics
ISBN: 9789814749800

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This book presents, in a unitary frame and from a new perspective, the main concepts and results of one of the most fascinating branches of modern mathematics, namely differential equations, and offers the reader another point of view concerning a possible way to approach the problems of existence, uniqueness, approximation, and continuation of the solutions to a Cauchy problem. In addition, it contains simple introductions to some topics which are not usually included in classical textbooks: the exponential formula, conservation laws, generalized solutions, Caratheodory solutions, differential inclusions, variational inequalities, viability, invariance, and gradient systems. In this new edition, some typos have been corrected and two new topics have been added: Delay differential equations and differential equations subjected to nonlocal initial conditions. The bibliography has also been updated and expanded.

Essays in Mathematics and its Applications

Essays in Mathematics and its Applications
Author: Themistocles M. Rassias,Panos M. Pardalos
Publsiher: Springer
Total Pages: 663
Release: 2016-06-14
Genre: Mathematics
ISBN: 9783319313382

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This volume, dedicated to the eminent mathematician Vladimir Arnold, presents a collection of research and survey papers written on a large spectrum of theories and problems that have been studied or introduced by Arnold himself. Emphasis is given to topics relating to dynamical systems, stability of integrable systems, algebraic and differential topology, global analysis, singularity theory and classical mechanics. A number of applications of Arnold’s groundbreaking work are presented. This publication will assist graduate students and research mathematicians in acquiring an in-depth understanding and insight into a wide domain of research of an interdisciplinary nature.

Mathematical Analysis and Applications

Mathematical Analysis and Applications
Author: Vicentiu D. Radulescu,Constantin Niculescu (P.)
Publsiher: American Institute of Physics
Total Pages: 184
Release: 2006-05-25
Genre: Mathematics
ISBN: UOM:39015064105078

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This book comprises the proceedings of the International Conference on Mathematical Analysis and Applications, held in Craiova, Romania, 23-24 September 2005. The peer-reviewed papers presented here cover a range of topics at the interface between mathematical physics, numerical analysis, optimal control, and calculus of variations. The coverage includes nonlinear analysis and partial differential equations as well as classical mathematical analysis and dynamical systems.

Stochastic Analysis Control Optimization and Applications

Stochastic Analysis  Control  Optimization and Applications
Author: William M. McEneaney,G. George Yin,Qing Zhang
Publsiher: Springer Science & Business Media
Total Pages: 660
Release: 2012-12-06
Genre: Technology & Engineering
ISBN: 9781461217848

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In view of Professor Wendell Fleming's many fundamental contributions, his profound influence on the mathematical and systems theory communi ties, his service to the profession, and his dedication to mathematics, we have invited a number of leading experts in the fields of control, optimiza tion, and stochastic systems to contribute to this volume in his honor on the occasion of his 70th birthday. These papers focus on various aspects of stochastic analysis, control theory and optimization, and applications. They include authoritative expositions and surveys as well as research papers on recent and important issues. The papers are grouped according to the following four major themes: (1) large deviations, risk sensitive and Hoc control, (2) partial differential equations and viscosity solutions, (3) stochastic control, filtering and parameter esti mation, and (4) mathematical finance and other applications. We express our deep gratitude to all of the authors for their invaluable contributions, and to the referees for their careful and timely reviews. We thank Harold Kushner for having graciously agreed to undertake the task of writing the foreword. Particular thanks go to H. Thomas Banks for his help, advice and suggestions during the entire preparation process, as well as for the generous support of the Center for Research in Scientific Computation. The assistance from the Birkhauser professional staff is also greatly appreciated.

Functional Differential Equations

Functional Differential Equations
Author: Constantin Corduneanu,Yizeng Li,Mehran Mahdavi
Publsiher: John Wiley & Sons
Total Pages: 368
Release: 2016-03-30
Genre: Mathematics
ISBN: 9781119189497

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Features new results and up-to-date advances in modeling and solving differential equations Introducing the various classes of functional differential equations, Functional Differential Equations: Advances and Applications presents the needed tools and topics to study the various classes of functional differential equations and is primarily concerned with the existence, uniqueness, and estimates of solutions to specific problems. The book focuses on the general theory of functional differential equations, provides the requisite mathematical background, and details the qualitative behavior of solutions to functional differential equations. The book addresses problems of stability, particularly for ordinary differential equations in which the theory can provide models for other classes of functional differential equations, and the stability of solutions is useful for the application of results within various fields of science, engineering, and economics. Functional Differential Equations: Advances and Applications also features: • Discussions on the classes of equations that cannot be solved to the highest order derivative, and in turn, addresses existence results and behavior types • Oscillatory motion and solutions that occur in many real-world phenomena as well as in man-made machines • Numerous examples and applications with a specific focus on ordinary differential equations and functional differential equations with finite delay • An appendix that introduces generalized Fourier series and Fourier analysis after periodicity and almost periodicity • An extensive Bibliography with over 550 references that connects the presented concepts to further topical exploration Functional Differential Equations: Advances and Applications is an ideal reference for academics and practitioners in applied mathematics, engineering, economics, and physics. The book is also an appropriate textbook for graduate- and PhD-level courses in applied mathematics, differential and difference equations, differential analysis, and dynamics processes. CONSTANTIN CORDUNEANU, PhD, is Emeritus Professor in the Department of Mathematics at The University of Texas at Arlington, USA. The author of six books and over 200 journal articles, he is currently Associate Editor for seven journals; a member of the American Mathematical Society, Society for Industrial and Applied Mathematics, and the Romanian Academy; and past president of the American Romanian Academy of Arts and Sciences. YIZENG LI, PhD, is Professor in the Department of Mathematics at Tarrant County College, USA. He is a member of the Society for Industrial and Applied Mathematics. MEHRAN MAHDAVI, PhD, is Professor in the Department of Mathematics at Bowie State University, USA. The author of numerous journal articles, he is a member of the American Mathematical Society, Society for Industrial and Applied Mathematics, and the Mathematical Association of America.

Current Research in Nonlinear Analysis

Current Research in Nonlinear Analysis
Author: Themistocles M. Rassias
Publsiher: Springer
Total Pages: 360
Release: 2018-06-18
Genre: Mathematics
ISBN: 9783319898001

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Current research and applications in nonlinear analysis influenced by Haim Brezis and Louis Nirenberg are presented in this book by leading mathematicians. Each contribution aims to broaden reader’s understanding of theories, methods, and techniques utilized to solve significant problems. Topics include: Sobolev Spaces Maximal monotone operators A theorem of Brezis-Nirenberg Operator-norm convergence of the Trotter product formula Elliptic operators with infinitely many variables Pseudo-and quasiconvexities for nonsmooth function Anisotropic surface measures Eulerian and Lagrangian variables Multiple periodic solutions of Lagrangian systems Porous medium equation Nondiscrete Lassonde-Revalski principle Graduate students and researchers in mathematics, physics, engineering, and economics will find this book a useful reference for new techniques and research areas. Haim Brezis and Louis Nirenberg’s fundamental research in nonlinear functional analysis and nonlinear partial differential equations along with their years of teaching and training students have had a notable impact in the field.