Differential Equations On Measures And Functional Spaces
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Differential Equations On Measures And Functional Spaces
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Author : Vassili Kolokoltsov
language : en
Publisher: Springer
Release Date : 2019-06-20
Differential Equations On Measures And Functional Spaces written by Vassili Kolokoltsov and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-06-20 with Mathematics categories.
This advanced book focuses on ordinary differential equations (ODEs) in Banach and more general locally convex spaces, most notably the ODEs on measures and various function spaces. It briefly discusses the fundamentals before moving on to the cutting edge research in linear and nonlinear partial and pseudo-differential equations, general kinetic equations and fractional evolutions. The level of generality chosen is suitable for the study of the most important nonlinear equations of mathematical physics, such as Boltzmann, Smoluchovskii, Vlasov, Landau-Fokker-Planck, Cahn-Hilliard, Hamilton-Jacobi-Bellman, nonlinear Schroedinger, McKean-Vlasov diffusions and their nonlocal extensions, mass-action-law kinetics from chemistry. It also covers nonlinear evolutions arising in evolutionary biology and mean-field games, optimization theory, epidemics and system biology, in general models of interacting particles or agents describing splitting and merging, collisions and breakage, mutations and the preferential-attachment growth on networks. The book is intended mainly for upper undergraduate and graduate students, but is also of use to researchers in differential equations and their applications. It particularly highlights the interconnections between various topics revealing where and how a particular result is used in other chapters or may be used in other contexts, and also clarifies the links between the languages of pseudo-differential operators, generalized functions, operator theory, abstract linear spaces, fractional calculus and path integrals.
Advances In Nonlinear Analysis Via The Concept Of Measure Of Noncompactness
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Author : Józef Banaś
language : en
Publisher: Springer
Release Date : 2017-04-25
Advances In Nonlinear Analysis Via The Concept Of Measure Of Noncompactness written by Józef Banaś and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-04-25 with Mathematics categories.
This book offers a comprehensive treatment of the theory of measures of noncompactness. It discusses various applications of the theory of measures of noncompactness, in particular, by addressing the results and methods of fixed-point theory. The concept of a measure of noncompactness is very useful for the mathematical community working in nonlinear analysis. Both these theories are especially useful in investigations connected with differential equations, integral equations, functional integral equations and optimization theory. Thus, one of the book’s central goals is to collect and present sufficient conditions for the solvability of such equations. The results are established in miscellaneous function spaces, and particular attention is paid to fractional calculus.
Measure Valued Solutions For Nonlinear Evolution Equations On Banach Spaces And Their Optimal Control
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Author : N. U. Ahmed
language : en
Publisher: Springer Nature
Release Date : 2023-09-12
Measure Valued Solutions For Nonlinear Evolution Equations On Banach Spaces And Their Optimal Control written by N. U. Ahmed and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-09-12 with Mathematics categories.
This book offers the first comprehensive presentation of measure-valued solutions for nonlinear deterministic and stochastic evolution equations on infinite dimensional Banach spaces. Unlike traditional solutions, measure-valued solutions allow for a much broader class of abstract evolution equations to be addressed, providing a broader approach. The book presents extensive results on the existence of measure-valued solutions for differential equations that have no solutions in the usual sense. It covers a range of topics, including evolution equations with continuous/discontinuous vector fields, neutral evolution equations subject to vector measures as impulsive forces, stochastic evolution equations, and optimal control of evolution equations. The optimal control problems considered cover the existence of solutions, necessary conditions of optimality, and more, significantly complementing the existing literature. This book will be of great interest to researchers in functional analysis, partial differential equations, dynamic systems and their optimal control, and their applications, advancing previous research and providing a foundation for further exploration of the field.
Functional Spaces For The Theory Of Elliptic Partial Differential Equations
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Author : Françoise Demengel
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-01-24
Functional Spaces For The Theory Of Elliptic Partial Differential Equations written by Françoise Demengel 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 2012-01-24 with Mathematics categories.
The theory of elliptic boundary problems is fundamental in analysis and the role of spaces of weakly differentiable functions (also called Sobolev spaces) is essential in this theory as a tool for analysing the regularity of the solutions. This book offers on the one hand a complete theory of Sobolev spaces, which are of fundamental importance for elliptic linear and non-linear differential equations, and explains on the other hand how the abstract methods of convex analysis can be combined with this theory to produce existence results for the solutions of non-linear elliptic boundary problems. The book also considers other kinds of functional spaces which are useful for treating variational problems such as the minimal surface problem. The main purpose of the book is to provide a tool for graduate and postgraduate students interested in partial differential equations, as well as a useful reference for researchers active in the field. Prerequisites include a knowledge of classical analysis, differential calculus, Banach and Hilbert spaces, integration and the related standard functional spaces, as well as the Fourier transformation on the Schwartz space. There are complete and detailed proofs of almost all the results announced and, in some cases, more than one proof is provided in order to highlight different features of the result. Each chapter concludes with a range of exercises of varying levels of difficulty, with hints to solutions provided for many of them.
Measure Theory And Nonlinear Evolution Equations
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Author : Flavia Smarrazzo
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2022-04-19
Measure Theory And Nonlinear Evolution Equations written by Flavia Smarrazzo 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 2022-04-19 with Mathematics categories.
This carefully written text on measure theory with applications to partial differential equations covers general measure theory, Lebesgue spaces of real-valued and vector-valued functions, different notions of measurability for the latter, weak convergence of functions and measures, Radon and Young measures, capacity, and finally applications to quasilinear parabolic problems (in particular, forward-backward equations).
Measure Of Noncompactness Fixed Point Theorems And Applications
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Author : S. A. Mohiuddine
language : en
Publisher: CRC Press
Release Date : 2024-04-24
Measure Of Noncompactness Fixed Point Theorems And Applications written by S. A. Mohiuddine and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-04-24 with Mathematics categories.
The theory of the measure of noncompactness has proved its significance in various contexts, particularly in the study of fixed point theory, differential equations, functional equations, integral and integrodifferential equations, optimization, and others. This edited volume presents the recent developments in the theory of the measure of noncompactness and its applications in pure and applied mathematics. It discusses important topics such as measures of noncompactness in the space of regulated functions, application in nonlinear infinite systems of fractional differential equations, and coupled fixed point theorem. Key Highlights: • Explains numerical solution of functional integral equation through coupled fixed point theorem, measure of noncompactness and iterative algorithm • Showcases applications of the measure of noncompactness and Petryshyn’s fixed point theorem functional integral equations in Banach algebra • Explores the existence of solutions of the implicit fractional integral equation via extension of the Darbo’s fixed point theorem • Discusses best proximity point results using measure of noncompactness and its applications • Includes solvability of some fractional differential equations in the holder space and their numerical treatment via measures of noncompactness This reference work is for scholars and academic researchers in pure and applied mathematics.
Stochastic Integration In Banach Spaces
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Author : Vidyadhar Mandrekar
language : en
Publisher: Springer
Release Date : 2014-12-03
Stochastic Integration In Banach Spaces written by Vidyadhar Mandrekar and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-12-03 with Mathematics categories.
Considering Poisson random measures as the driving sources for stochastic (partial) differential equations allows us to incorporate jumps and to model sudden, unexpected phenomena. By using such equations the present book introduces a new method for modeling the states of complex systems perturbed by random sources over time, such as interest rates in financial markets or temperature distributions in a specific region. It studies properties of the solutions of the stochastic equations, observing the long-term behavior and the sensitivity of the solutions to changes in the initial data. The authors consider an integration theory of measurable and adapted processes in appropriate Banach spaces as well as the non-Gaussian case, whereas most of the literature only focuses on predictable settings in Hilbert spaces. The book is intended for graduate students and researchers in stochastic (partial) differential equations, mathematical finance and non-linear filtering and assumes a knowledge of the required integration theory, existence and uniqueness results and stability theory. The results will be of particular interest to natural scientists and the finance community. Readers should ideally be familiar with stochastic processes and probability theory in general, as well as functional analysis and in particular the theory of operator semigroups.
Handbook Of Functional Equations
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Author : Themistocles M. Rassias
language : en
Publisher: Springer
Release Date : 2014-11-21
Handbook Of Functional Equations written by Themistocles M. Rassias and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-11-21 with Mathematics categories.
This handbook consists of seventeen chapters written by eminent scientists from the international mathematical community, who present important research works in the field of mathematical analysis and related subjects, particularly in the Ulam stability theory of functional equations. The book provides an insight into a large domain of research with emphasis to the discussion of several theories, methods and problems in approximation theory, analytic inequalities, functional analysis, computational algebra and applications. The notion of stability of functional equations has its origins with S. M. Ulam, who posed the fundamental problem for approximate homomorphisms in 1940 and with D. H. Hyers, Th. M. Rassias, who provided the first significant solutions for additive and linear mappings in 1941 and 1978, respectively. During the last decade the notion of stability of functional equations has evolved into a very active domain of mathematical research with several applications of interdisciplinary nature. The chapters of this handbook focus mainly on both old and recent developments on the equation of homomorphism for square symmetric groupoids, the linear and polynomial functional equations in a single variable, the Drygas functional equation on amenable semigroups, monomial functional equation, the Cauchy–Jensen type mappings, differential equations and differential operators, operational equations and inclusions, generalized module left higher derivations, selections of set-valued mappings, D’Alembert’s functional equation, characterizations of information measures, functional equations in restricted domains, as well as generalized functional stability and fixed point theory.
Eleven Papers On Differential Equations Functional Analysis And Measure Theory
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Author :
language : en
Publisher: American Mathematical Soc.
Release Date : 1966
Eleven Papers On Differential Equations Functional Analysis And Measure Theory written by 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 1966 with Differential equations categories.
Morrey Spaces
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Author : Yoshihiro Sawano
language : en
Publisher: CRC Press
Release Date : 2020-09-17
Morrey Spaces written by Yoshihiro Sawano and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-09-17 with Mathematics categories.
Morrey spaces were introduced by Charles Morrey to investigate the local behaviour of solutions to second order elliptic partial differential equations. The technique is very useful in many areas in mathematics, in particular in harmonic analysis, potential theory, partial differential equations and mathematical physics. Across two volumes, the authors of Morrey Spaces: Introduction and Applications to Integral Operators and PDE’s discuss the current state of art and perspectives of developments of this theory of Morrey spaces, with the emphasis in Volume I focused mainly on harmonic analysis. Features Provides a ‘from-scratch’ overview of the topic readable by anyone with an understanding of integration theory Suitable for graduate students, masters course students, and researchers in PDE's or Geometry Replete with exercises and examples to aid the reader’s understanding