Advanced Topics On Semilinear Evolution Equations
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Advanced Topics On Semilinear Evolution Equations
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Author : Mouffak Benchohra
language : en
Publisher: World Scientific
Release Date : 2025-01-07
Advanced Topics On Semilinear Evolution Equations written by Mouffak Benchohra and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-01-07 with Mathematics categories.
Differential evolution equations serve as mathematical representations that capture the progression or transformation of functions or systems as time passes. Currently, differential equations continue to be an active and thriving area of study, with continuous advancements in mathematical methodologies and their practical applications spanning diverse fields such as physics, engineering, and economics. In the late 20th century, the notion of 'Differential Evolution Equations' emerged as a distinct field applied to optimization and machine learning challenges. Evolution equations hold immense importance in numerous realms of applied mathematics and have experienced notable prominence in recent times.This book delves into the study of several classes of equations, aiming to investigate the existence of mild and periodic mild solutions and their properties such as approximate controllability, complete controllability and attractivity, under various conditions. By examining diverse problems involving second-order semilinear evolution equations, differential and integro-differential equations with state-dependent delay, random effects, and functional differential equations with delay and random effects, we hope to contribute to the advancement of mathematical knowledge and provide researchers, academicians, and students with a solid foundation for further exploration in this field. Throughout this book, we explore different mathematical frameworks, employing Fréchet spaces and Banach spaces to provide a comprehensive analysis. Our investigation extends beyond traditional solutions, encompassing the study of asymptotically almost automorphic mild solutions, periodic mild solutions, and impulsive integro-differential equations. These topics shed light on the behavior of equations in both bounded and unbounded domains, offering valuable insights into the dynamics of functional evolution equations.
Advanced Topics On Semilinear Evolution Equations
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Author : GASTON MANDATA. BENCHOHRA N'GUEREKATA (MOUFFAK. SALIM, ABDELKRIM.)
language : en
Publisher: World Scientific Publishing Company
Release Date : 2025-02-07
Advanced Topics On Semilinear Evolution Equations written by GASTON MANDATA. BENCHOHRA N'GUEREKATA (MOUFFAK. SALIM, ABDELKRIM.) and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-02-07 with Mathematics categories.
Differential evolution equations serve as mathematical representations that capture the progression or transformation of functions or systems as time passes. Currently, differential equations continue to be an active and thriving area of study, with continuous advancements in mathematical methodologies and their practical applications spanning diverse fields such as physics, engineering, and economics. In the late 20th century, the notion of 'Differential Evolution Equations' emerged as a distinct field applied to optimization and machine learning challenges. Evolution equations hold immense importance in numerous realms of applied mathematics and have experienced notable prominence in recent times.This book delves into the study of several classes of equations, aiming to investigate the existence of mild and periodic mild solutions and their properties such as approximate controllability, complete controllability and attractivity, under various conditions. By examining diverse problems involving second-order semilinear evolution equations, differential and integro-differential equations with state-dependent delay, random effects, and functional differential equations with delay and random effects, we hope to contribute to the advancement of mathematical knowledge and provide researchers, academicians, and students with a solid foundation for further exploration in this field. Throughout this book, we explore different mathematical frameworks, employing Fréchet spaces and Banach spaces to provide a comprehensive analysis. Our investigation extends beyond traditional solutions, encompassing the study of asymptotically almost automorphic mild solutions, periodic mild solutions, and impulsive integro-differential equations. These topics shed light on the behavior of equations in both bounded and unbounded domains, offering valuable insights into the dynamics of functional evolution equations.
Strong And Weak Approximation Of Semilinear Stochastic Evolution Equations
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Author : Raphael Kruse
language : en
Publisher: Springer
Release Date : 2013-11-18
Strong And Weak Approximation Of Semilinear Stochastic Evolution Equations written by Raphael Kruse and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-18 with Mathematics categories.
In this book we analyze the error caused by numerical schemes for the approximation of semilinear stochastic evolution equations (SEEq) in a Hilbert space-valued setting. The numerical schemes considered combine Galerkin finite element methods with Euler-type temporal approximations. Starting from a precise analysis of the spatio-temporal regularity of the mild solution to the SEEq, we derive and prove optimal error estimates of the strong error of convergence in the first part of the book. The second part deals with a new approach to the so-called weak error of convergence, which measures the distance between the law of the numerical solution and the law of the exact solution. This approach is based on Bismut’s integration by parts formula and the Malliavin calculus for infinite dimensional stochastic processes. These techniques are developed and explained in a separate chapter, before the weak convergence is proven for linear SEEq.
Advanced Topics In Scattering And Biomedical Engineering
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Author : A. Charalambopoulos
language : en
Publisher: World Scientific
Release Date : 2008
Advanced Topics In Scattering And Biomedical Engineering written by A. Charalambopoulos and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Medical categories.
This volume of proceedings consists of the papers presented during the 8th International Workshop on Mathematical Methods in Scattering Theory and Biomedical Engineering, held in Lefkada, Greece, on 27-29 September 2007.The book contains papers on scattering theory and biomedical engineering ? two rapidly evolving fields which have a considerable impact on today's research. All the papers are state-of-the-art, have been carefully reviewed before publication and the authors are well-known in the scientific community. In addition, some papers focus more on applied mathematics, which is the solid ground for development and innovative research in scattering and biomedical engineering.
Advanced Topics In Scattering And Biomedical Engineering
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Author : Dimitrios Ioannou Fotiadis
language : en
Publisher: World Scientific
Release Date : 2008
Advanced Topics In Scattering And Biomedical Engineering written by Dimitrios Ioannou Fotiadis and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Medical categories.
This volume of proceedings consists of the papers presented during the 8th International Workshop on Mathematical Methods in Scattering Theory and Biomedical Engineering, held in Lefkada, Greece, on 27-29 September 2007. The book contains papers on scattering theory and biomedical engineering - two rapidly evolving fields which have a considerable impact on today's research. All the papers are state-of-the-art, have been carefully reviewed before publication and the authors are well-known in the scientific community. In addition, some papers focus more on applied mathematics, which is the solid ground for development and innovative research in scattering and biomedical engineering.
Integro Differential Equations
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Author : Mouffak Benchohra
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2024-08-19
Integro Differential Equations written by Mouffak Benchohra 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 2024-08-19 with Technology & Engineering categories.
This book delves into semilinear evolution equations, impulsive differential equations, and integro-differential equations with different types of delay. The main objective is to investigate the existence of solutions and explore their approximate controllability, complete controllability, and attractivity. The study involves boundary conditions, nonlocal conditions, and impulsive conditions. The analysis presented in this book goes beyond traditional solutions and encompasses the study of solutions that are asymptotically almost automorphic and integro-differential equations with impulsive effects in both bounded and unbounded domains. The book also contains applications to nuclear physics, elementary particle physics, chemical engineering, and economics. This book is intended for researchers and professionals in the field of mathematics, physics and industrial engineering, as well as advanced graduate students.
Evolution Equations And Approximations
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Author : Kazufumi Ito
language : en
Publisher: World Scientific
Release Date : 2002
Evolution Equations And Approximations written by Kazufumi Ito and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Science categories.
Annotation Ito (North Carolina State U.) and Kappel (U. of Graz, Austria) offer a unified presentation of the general approach for well-posedness results using abstract evolution equations, drawing from and modifying the work of K. and Y. Kobayashi and S. Oharu. They also explore abstract approximation results for evolution equations. Their work is not a textbook, but they explain how instructors can use various sections, or combinations of them, as a foundation for a range of courses. Annotation copyrighted by Book News, Inc., Portland, OR
Fractional Differential Equations And Inclusions Classical And Advanced Topics
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Author : Said Abbas
language : en
Publisher: World Scientific
Release Date : 2023-02-02
Fractional Differential Equations And Inclusions Classical And Advanced Topics written by Said Abbas and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-02-02 with Mathematics categories.
This monograph is devoted to the existence and stability (Ulam-Hyers-Rassias stability and asymptotic stability) of solutions for various classes of functional differential equations or inclusions involving the Hadamard or Hilfer fractional derivative. Some equations present delay which may be finite, infinite, or state-dependent. Others are subject to impulsive effect which may be fixed or non-instantaneous.Readers will find the book self-contained and unified in presentation. It provides the necessary background material required to go further into the subject and explores the rich research literature in detail. Each chapter concludes with a section devoted to notes and bibliographical remarks and all abstract results are illustrated by examples. The tools used include many classical and modern nonlinear analysis methods such as fixed-point theorems, as well as some notions of Ulam stability, attractivity and the measure of non-compactness as well as the measure of weak noncompactness. It is useful for researchers and graduate students for research, seminars, and advanced graduate courses, in pure and applied mathematics, physics, mechanics, engineering, biology, and all other applied sciences.
Blow Up Theories For Semilinear Parabolic Equations
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Author : Bei Hu
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-03-23
Blow Up Theories For Semilinear Parabolic Equations written by Bei Hu 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 2011-03-23 with Mathematics categories.
There is an enormous amount of work in the literature about the blow-up behavior of evolution equations. It is our intention to introduce the theory by emphasizing the methods while seeking to avoid massive technical computations. To reach this goal, we use the simplest equation to illustrate the methods; these methods very often apply to more general equations.
Selected Topics In Almost Periodicity
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Author : Marko Kostić
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2021-11-22
Selected Topics In Almost Periodicity written by Marko Kostić 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 2021-11-22 with Mathematics categories.
Covers uniformly recurrent solutions and c-almost periodic solutions of abstract Volterra integro-differential equations as well as various generalizations of almost periodic functions in Lebesgue spaces with variable coefficients. Treats multi-dimensional almost periodic type functions and their generalizations in adequate detail.