Theory and Applications of Abstract Semilinear Cauchy Problems PDF Download

Author: Pierre Magal
Publisher: Springer
ISBN: 3030015068
Category : Mathematics
Languages : en
Pages : 558

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Book Description
Several types of differential equations, such as functional differential equation, age-structured models, transport equations, reaction-diffusion equations, and partial differential equations with delay, can be formulated as abstract Cauchy problems with non-dense domain. This monograph provides a self-contained and comprehensive presentation of the fundamental theory of non-densely defined semilinear Cauchy problems and their applications. Starting from the classical Hille-Yosida theorem, semigroup method, and spectral theory, this monograph introduces the abstract Cauchy problems with non-dense domain, integrated semigroups, the existence of integrated solutions, positivity of solutions, Lipschitz perturbation, differentiability of solutions with respect to the state variable, and time differentiability of solutions. Combining the functional analysis method and bifurcation approach in dynamical systems, then the nonlinear dynamics such as the stability of equilibria, center manifold theory, Hopf bifurcation, and normal form theory are established for abstract Cauchy problems with non-dense domain. Finally applications to functional differential equations, age-structured models, and parabolic equations are presented. This monograph will be very valuable for graduate students and researchers in the fields of abstract Cauchy problems, infinite dimensional dynamical systems, and their applications in biological, chemical, medical, and physical problems.

Author: Toka Diagana
Publisher: Springer
ISBN: 303000449X
Category : Mathematics
Languages : en
Pages : 199

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Book Description
This book, which is a continuation of Almost Automorphic Type and Almost Periodic Type Functions in Abstract Spaces, presents recent trends and developments upon fractional, first, and second order semilinear difference and differential equations, including degenerate ones. Various stability, uniqueness, and existence results are established using various tools from nonlinear functional analysis and operator theory (such as semigroup methods). Various applications to partial differential equations and the dynamic of populations are amply discussed. This self-contained volume is primarily intended for advanced undergraduate and graduate students, post-graduates and researchers, but may also be of interest to non-mathematicians such as physicists and theoretically oriented engineers. It can also be used as a graduate text on evolution equations and difference equations and their applications to partial differential equations and practical problems arising in population dynamics. For completeness, detailed preliminary background on Banach and Hilbert spaces, operator theory, semigroups of operators, and almost periodic functions and their spectral theory are included as well.

Author: J. C. Meyer
Publisher: Cambridge University Press
ISBN: 1107477395
Category : Mathematics
Languages : en
Pages : 177

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Book Description
A monograph containing significant new developments in the theory of reaction-diffusion systems, particularly those arising in chemistry and life sciences.

Author: A. Belleni-Morante
Publisher: John Wiley & Sons
ISBN:
Category : Mathematics
Languages : en
Pages : 298

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Book Description
Mathematical Methods in Practice Advisory Editors Bruno Brosowski Universität Frankfurt Germany Gary F. Roach University of Strathclyde UK Volume 3 Applied Nonlinear Semigroups A. Belleni-Morante University of Florence, Italy A. C. McBride University of Strathclyde, UK In many disciplines such as physics, chemistry, biology, meteorology, electronics and economics, it is increasingly necessary to develop mathematical models that describe how the state of a system evolves with time. A useful way of studying such a model is to recast the appropriate evolution equation as an Abstract Cauchy Problem (ACP), which can then be analysed via the powerful theory of semigroups of operators. The user-friendly presentation in the book is centred on Abstract Cauchy Problems which model various processes such as particle transport,diffusion and combustion, all of which are examples of systems which evolve with time. The authors provide an introduction to the requisite concepts from functional analysis before moving on to the theory of semigroups of linear operators and their application to linear ACPs. These ideas are then applied to semilinear problems and fully nonlinear problems and it is shown how results from the linear theory can be extended. Finally, a variety of applications of practical interest are included. By leading a non-expert to the solutions of problems involving evolution equations via the theory of semigroups of operators, both linear and nonlinear, the book provides an accessible introduction to the treatment of the subject. The reader is assumed to have a basic knowledge of real analysis and vector spaces. M.Sc. and graduate students of functional analysis, applied mathematics, physics and engineering will find this an invaluable introduction to the subject.

Author: Athanass Kartsatos
Publisher: CRC Press
ISBN: 9780824797218
Category : Mathematics
Languages : en
Pages : 338

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Book Description
This work is based upon a Special Session on the Theory and Applications of Nonlinear Operators of Accretive and Monotone Type held during the recent meeting of the American Mathematical Society in San Francisco. It examines current developments in non-linear analysis, emphasizing accretive and monotone operator theory. The book presents a major survey/research article on partial functional differential equations with delay and an important survey/research article on approximation solvability.

Author: Marko Kostić
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110641259
Category : Mathematics
Languages : en
Pages : 372

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Book Description
This book discusses almost periodic and almost automorphic solutions to abstract integro-differential Volterra equations that are degenerate in time, and in particular equations whose solutions are governed by (degenerate) solution operator families with removable singularities at zero. It particularly covers abstract fractional equations and inclusions with multivalued linear operators as well as abstract fractional semilinear Cauchy problems.

Author: D Daners
Publisher: Chapman and Hall/CRC
ISBN:
Category : Mathematics
Languages : en
Pages : 268

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Book Description
Part of the Pitman Research Notes in Mathematics series, this text covers: linear evolution equations of parabolic type; semilinear evolution equations of parabolic type; evolution equations and positivity; semilinear periodic evolution equations; and applications.

Author: Jan Prüss
Publisher: Springer Science & Business Media
ISBN: 3034804997
Category : Mathematics
Languages : en
Pages : 391

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Book Description
This book deals with evolutionary systems whose equation of state can be formulated as a linear Volterra equation in a Banach space. The main feature of the kernels involved is that they consist of unbounded linear operators. The aim is a coherent presentation of the state of art of the theory including detailed proofs and its applications to problems from mathematical physics, such as viscoelasticity, heat conduction, and electrodynamics with memory. The importance of evolutionary integral equations ‒ which form a larger class than do evolution equations​ ‒ stems from such applications and therefore special emphasis is placed on these. A number of models are derived and, by means of the developed theory, discussed thoroughly. An annotated bibliography containing 450 entries increases the book’s value as an incisive reference text. --- This excellent book presents a general approach to linear evolutionary systems, with an emphasis on infinite-dimensional systems with time delays, such as those occurring in linear viscoelasticity with or without thermal effects. It gives a very natural and mature extension of the usual semigroup approach to a more general class of infinite-dimensional evolutionary systems. This is the first appearance in the form of a monograph of this recently developed theory. A substantial part of the results are due to the author, or are even new. (...) It is not a book that one reads in a few days. Rather, it should be considered as an investment with lasting value. (Zentralblatt MATH) In this book, the author, who has been at the forefront of research on these problems for the last decade, has collected, and in many places extended, the known theory for these equations. In addition, he has provided a framework that allows one to relate and evaluate diverse results in the literature. (Mathematical Reviews) This book constitutes a highly valuable addition to the existing literature on the theory of Volterra (evolutionary) integral equations and their applications in physics and engineering. (...) and for the first time the stress is on the infinite-dimensional case. (SIAM Reviews)

Author: J. Prüss
Publisher: Birkhäuser
ISBN: 3034885709
Category : Science
Languages : en
Pages : 393

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Book Description
During the last two decades the theory of abstract Volterra equations has under gone rapid development. To a large extent this was due to the applications of this theory to problems in mathematical physics, such as viscoelasticity, heat conduc tion in materials with memory, electrodynamics with memory, and to the need of tools to tackle the problems arising in these fields. Many interesting phenomena not found with differential equations but observed in specific examples of Volterra type stimulated research and improved our understanding and knowledge. Al though this process is still going on, in particular concerning nonlinear problems, the linear theory has reached a state of maturity. In recent years several good books on Volterra equations have appeared. How ever, none of them accounts for linear problems in infinite dimensions, and there fore this part of the theory has been available only through the - meanwhile enor mous - original literature, so far. The present monograph intends to close this gap. Its aim is a coherent exposition of the state of the art in the linear theory. It brings together and unifies most of the relevant results available at present, and should ease the way through the original literature for anyone intending to work on abstract Volterra equations and its applications. And it exhibits many prob lems in the linear theory which have not been solved or even not been considered, so far.

Author: Sandeep Singh
Publisher: CRC Press
ISBN: 1040152228
Category : Technology & Engineering
Languages : en
Pages : 189

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Book Description
Currently, the techniques of operation research are widely used in every aspect of day-to-day life. This book discusses a variety of problems that arise in various businesses and develops mathematical theories as well as technology answers to solve them from an industry perspective. Optimization Techniques and Associated Applications incorporates cutting-edge methods for locating early workable answers to an optimization challenge and acts as a road map for creating a catastrophe management paradigm that is sustainable. This book offers numerical methods for resolving mathematical issues that can be found in numerous sectors and includes specific case studies of actual industrial optimization applications. The uncertainty that arises in various businesses is explored and new and recently developed techniques are discussed. Because this book primarily focuses on operations research and solutions to the challenges across a variety of disciplines, the audience is expansive and can include professionals, students, and researchers from mathematics as well as engineers from industrial engineering, computer science, information technology, mechanical, civil, electrical, petroleum, chemical, aerospace, aviation, meteorology, disaster management, and other departments.