Non Local Partial Differential Equations For Engineering And Biology
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Non Local Partial Differential Equations For Engineering And Biology
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Author : Nikos I. Kavallaris
language : en
Publisher: Springer
Release Date : 2017-11-28
Non Local Partial Differential Equations For Engineering And Biology written by Nikos I. Kavallaris and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-28 with Technology & Engineering categories.
This book presents new developments in non-local mathematical modeling and mathematical analysis on the behavior of solutions with novel technical tools. Theoretical backgrounds in mechanics, thermo-dynamics, game theory, and theoretical biology are examined in details. It starts off with a review and summary of the basic ideas of mathematical modeling frequently used in the sciences and engineering. The authors then employ a number of models in bio-science and material science to demonstrate applications, and provide recent advanced studies, both on deterministic non-local partial differential equations and on some of their stochastic counterparts used in engineering. Mathematical models applied in engineering, chemistry, and biology are subject to conservation laws. For instance, decrease or increase in thermodynamic quantities and non-local partial differential equations, associated with the conserved physical quantities as parameters. These present novel mathematical objects are engaged with rich mathematical structures, in accordance with the interactions between species or individuals, self-organization, pattern formation, hysteresis. These models are based on various laws of physics, such as mechanics of continuum, electro-magnetic theory, and thermodynamics. This is why many areas of mathematics, calculus of variation, dynamical systems, integrable systems, blow-up analysis, and energy methods are indispensable in understanding and analyzing these phenomena. This book aims for researchers and upper grade students in mathematics, engineering, physics, economics, and biology.
Input To State Stability For Pdes
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Author : Iasson Karafyllis
language : en
Publisher: Springer
Release Date : 2018-06-07
Input To State Stability For Pdes written by Iasson Karafyllis and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-06-07 with Technology & Engineering categories.
This book lays the foundation for the study of input-to-state stability (ISS) of partial differential equations (PDEs) predominantly of two classes—parabolic and hyperbolic. This foundation consists of new PDE-specific tools. In addition to developing ISS theorems, equipped with gain estimates with respect to external disturbances, the authors develop small-gain stability theorems for systems involving PDEs. A variety of system combinations are considered: PDEs (of either class) with static maps; PDEs (again, of either class) with ODEs; PDEs of the same class (parabolic with parabolic and hyperbolic with hyperbolic); and feedback loops of PDEs of different classes (parabolic with hyperbolic). In addition to stability results (including ISS), the text develops existence and uniqueness theory for all systems that are considered. Many of these results answer for the first time the existence and uniqueness problems for many problems that have dominated the PDE control literature of the last two decades, including—for PDEs that include non-local terms—backstepping control designs which result in non-local boundary conditions. Input-to-State Stability for PDEs will interest applied mathematicians and control specialists researching PDEs either as graduate students or full-time academics. It also contains a large number of applications that are at the core of many scientific disciplines and so will be of importance for researchers in physics, engineering, biology, social systems and others.
Superlinear Parabolic Problems
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Author : Prof. Dr. Pavol Quittner
language : en
Publisher: Springer
Release Date : 2019-06-13
Superlinear Parabolic Problems written by Prof. Dr. Pavol Quittner and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-06-13 with Mathematics categories.
This book is devoted to the qualitative study of solutions of superlinear elliptic and parabolic partial differential equations and systems. This class of problems contains, in particular, a number of reaction-diffusion systems which arise in various mathematical models, especially in chemistry, physics and biology. The first two chapters introduce to the field and enable the reader to get acquainted with the main ideas by studying simple model problems, respectively of elliptic and parabolic type. The subsequent three chapters are devoted to problems with more complex structure; namely, elliptic and parabolic systems, equations with gradient depending nonlinearities, and nonlocal equations. They include many developments which reflect several aspects of current research. Although the techniques introduced in the first two chapters provide efficient tools to attack some aspects of these problems, they often display new phenomena and specifically different behaviors, whosestudy requires new ideas. Many open problems are mentioned and commented. The book is self-contained and up-to-date, it has a high didactic quality. It is devoted to problems that are intensively studied but have not been treated so far in depth in the book literature. The intended audience includes graduate and postgraduate students and researchers working in the field of partial differential equations and applied mathematics. The first edition of this book has become one of the standard references in the field. This second edition provides a revised text and contains a number of updates reflecting significant recent advances that have appeared in this growing field since the first edition.
Stochastic Evolution Equations
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Author : Wilfried Grecksch
language : en
Publisher: De Gruyter Akademie Forschung
Release Date : 1995
Stochastic Evolution Equations written by Wilfried Grecksch and has been published by De Gruyter Akademie Forschung this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Mathematics categories.
The authors give a self-contained exposition of the theory of stochastic evolution equations. Elements of infinite dimensional analysis, martingale theory in Hilbert spaces, stochastic integrals, stochastic convolutions are applied. Existence and uniqueness theorems for stochastic evolution equations in Hilbert spaces in the sense of the semigroup theory, the theory of evolution operators, and monotonous operators in rigged Hilbert spaces are discussed. Relationships between the different concepts are demonstrated. The results are used to concrete stochastic partial differential equations like parabolic and hyperbolic Ito equations and random constitutive equations of elastic viscoplastic materials. Furthermore, stochastic evolution equations in rigged Hilbert spaces are approximated by time discretization methods.
Flow And Transport Properties Of Unconventional Reservoirs 2018
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Author : Jianchao Cai
language : en
Publisher: MDPI
Release Date : 2019-07-23
Flow And Transport Properties Of Unconventional Reservoirs 2018 written by Jianchao Cai and has been published by MDPI this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-07-23 with Technology & Engineering categories.
Unconventional reservoirs are usually complex and highly heterogeneous, such as shale, coal, and tight sandstone reservoirs. The strong physical and chemical interactions between fluids and pore surfaces lead to the inapplicability of conventional approaches for characterizing fluid flow in these low-porosity and ultralow-permeability reservoir systems. Therefore, new theories and techniques are urgently needed to characterize petrophysical properties, fluid transport, and their relationships at multiple scales for improving production efficiency from unconventional reservoirs. This book presents fundamental innovations gathered from 21 recent works on novel applications of new techniques and theories in unconventional reservoirs, covering the fields of petrophysical characterization, hydraulic fracturing, fluid transport physics, enhanced oil recovery, and geothermal energy. Clearly, the research covered in this book is helpful to understand and master the latest techniques and theories for unconventional reservoirs, which have important practical significance for the economic and effective development of unconventional oil and gas resources.
Mathematical Methods In Engineering
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Author : K. Tas
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-11-25
Mathematical Methods In Engineering written by K. Tas 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 2007-11-25 with Technology & Engineering categories.
This book contains some of the contributions that have been carefully selected and peer-reviewed, which were presented at the International Symposium MME06 Mathematical Methods in Engineering, held in Cankaya University, Ankara, April 2006. The Symposium provided a setting for discussing recent developments in Fractional Mathematics, Neutrices and Generalized Functions, Boundary Value Problems, Applications of Wavelets, Dynamical Systems and Control Theory.
Mathematical Methods In Medical And Biological Sciences
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Author : Harendra Singh
language : en
Publisher: Elsevier
Release Date : 2024-11-05
Mathematical Methods In Medical And Biological Sciences written by Harendra Singh and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-11-05 with Mathematics categories.
Mathematical Methods in Medical and Biological Sciences presents mathematical methods for computational models arising in the medical and biological sciences. The book presents several real-life medical and biological models, such as infectious and non-infectious diseases that can be modeled mathematically to accomplish profound research in virtual environments when the cost of laboratory expenses is relatively high. It focuses on mathematical techniques that provide global solutions for models arising in medical and biological sciences by considering their long-term benefits. In addition, the book provides leading-edge developments and insights for a range of applications, including epidemiological modeling of pandemic dynamics, viral infection developments, cancer developments, blood oxygen dynamics, HIV infection spread, reaction-diffusion models, polio infection spread, and chaos modeling with fractional order derivatives. - Presents the mathematical treatment of a wide range of real-life medical and biological models, including both infectious and non-infectious diseases - Provides in-depth analysis of the spread of Covid-19, polio, and HIV, including discussion of computational methods and applications - Includes computational modeling methods, along with their practical applications, providing the basis for further exploration and research in epidemiology and applied biomedical sciences
Fractional Calculus In Medical And Health Science
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Author : Devendra Kumar
language : en
Publisher: CRC Press
Release Date : 2020-07-09
Fractional Calculus In Medical And Health Science written by Devendra Kumar and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-07-09 with Mathematics categories.
This book covers applications of fractional calculus used for medical and health science. It offers a collection of research articles built into chapters on classical and modern dynamical systems formulated by fractional differential equations describing human diseases and how to control them. The mathematical results included in the book will be helpful to mathematicians and doctors by enabling them to explain real-life problems accurately. The book will also offer case studies of real-life situations with an emphasis on describing the mathematical results and showing how to apply the results to medical and health science, and at the same time highlighting modeling strategies. The book will be useful to graduate level students, educators and researchers interested in mathematics and medical science.
Intelligent Systems Concepts Methodologies Tools And Applications
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Author : Management Association, Information Resources
language : en
Publisher: IGI Global
Release Date : 2018-06-04
Intelligent Systems Concepts Methodologies Tools And Applications written by Management Association, Information Resources and has been published by IGI Global this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-06-04 with Computers categories.
Ongoing advancements in modern technology have led to significant developments in intelligent systems. With the numerous applications available, it becomes imperative to conduct research and make further progress in this field. Intelligent Systems: Concepts, Methodologies, Tools, and Applications contains a compendium of the latest academic material on the latest breakthroughs and recent progress in intelligent systems. Including innovative studies on information retrieval, artificial intelligence, and software engineering, this multi-volume book is an ideal source for researchers, professionals, academics, upper-level students, and practitioners interested in emerging perspectives in the field of intelligent systems.
Modeling Of Discrete And Continuous Systems
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Author : Mohamed Kharrat
language : en
Publisher: Springer Nature
Release Date : 2025-02-27
Modeling Of Discrete And Continuous Systems written by Mohamed Kharrat and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-02-27 with Mathematics categories.
This book contains a comprehensive collection of chapters on recent and original research, along with review articles, on mathematical modeling of dynamical systems described by various types of differential equations. Structured into 18 chapters dedicated to exploring different aspects of differential equations and their applications in modeling both discrete and continuous systems, it highlights theoretical advancements in mathematics and their practical applications in modeling dynamic systems. Readers will find contributions by renowned scholars who delve into the intricacies of nonlinear dynamics, stochastic processes, and partial differential equations. This book is an essential resource for researchers, academicians, and practitioners in the field of mathematical modeling.