Theory And Applications Of Abstract Semilinear Cauchy Problems

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Theory And Applications Of Abstract Semilinear Cauchy Problems

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Author : Pierre Magal
language : en
Publisher: Springer
Release Date : 2018-11-21

Theory And Applications Of Abstract Semilinear Cauchy Problems written by Pierre Magal and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-11-21 with Mathematics categories.

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.

Abstract Cauchy Problems

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Author : Irina V. Melnikova
language : en
Publisher: CRC Press
Release Date : 2001-03-27

Abstract Cauchy Problems written by Irina V. Melnikova and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-03-27 with Mathematics categories.

Although the theory of well-posed Cauchy problems is reasonably understood, ill-posed problems-involved in a numerous mathematical models in physics, engineering, and finance- can be approached in a variety of ways. Historically, there have been three major strategies for dealing with such problems: semigroup, abstract distribution, and regularizat

The Cauchy Problem For Higher Order Abstract Differential Equations

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Author : Ti-Jun Xiao
language : en
Publisher: Springer
Release Date : 2013-12-11

The Cauchy Problem For Higher Order Abstract Differential Equations written by Ti-Jun Xiao and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-11 with Mathematics categories.

The main purpose of this book is to present the basic theory and some recent de velopments concerning the Cauchy problem for higher order abstract differential equations u(n)(t) + ~ AiU(i)(t) = 0, t ~ 0, { U(k)(O) = Uk, 0 ~ k ~ n-l. where AQ, Ab . . . , A - are linear operators in a topological vector space E. n 1 Many problems in nature can be modeled as (ACP ). For example, many n initial value or initial-boundary value problems for partial differential equations, stemmed from mechanics, physics, engineering, control theory, etc. , can be trans lated into this form by regarding the partial differential operators in the space variables as operators Ai (0 ~ i ~ n - 1) in some function space E and letting the boundary conditions (if any) be absorbed into the definition of the space E or of the domain of Ai (this idea of treating initial value or initial-boundary value problems was discovered independently by E. Hille and K. Yosida in the forties). The theory of (ACP ) is closely connected with many other branches of n mathematics. Therefore, the study of (ACPn) is important for both theoretical investigations and practical applications. Over the past half a century, (ACP ) has been studied extensively.

Abstract Cauchy Problems

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Author : Irina V. Melnikova
language : en
Publisher: Chapman and Hall/CRC
Release Date : 2001-03-27

Abstract Cauchy Problems written by Irina V. Melnikova and has been published by Chapman and Hall/CRC this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-03-27 with Mathematics categories.

Although the theory of well-posed Cauchy problems is reasonably understood, ill-posed problems-involved in a numerous mathematical models in physics, engineering, and finance- can be approached in a variety of ways. Historically, there have been three major strategies for dealing with such problems: semigroup, abstract distribution, and regularization methods. Semigroup and distribution methods restore well-posedness, in a modern weak sense. Regularization methods provide approximate solutions to ill-posed problems. Although these approaches were extensively developed over the last decades by many researchers, nowhere could one find a comprehensive treatment of all three approaches. Abstract Cauchy Problems: Three Approaches provides an innovative, self-contained account of these methods and, furthermore, demonstrates and studies some of the profound connections between them. The authors discuss the application of different methods not only to the Cauchy problem that is not well-posed in the classical sense, but also to important generalizations: the Cauchy problem for inclusion and the Cauchy problem for second order equations. Accessible to nonspecialists and beginning graduate students, this volume brings together many different ideas to serve as a reference on modern methods for abstract linear evolution equations.

Theory And Applications Of Nonlinear Operators Of Accretive And Monotone Type

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Author : Athanass Kartsatos
language : en
Publisher: CRC Press
Release Date : 1996-03-14

Theory And Applications Of Nonlinear Operators Of Accretive And Monotone Type written by Athanass Kartsatos and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-03-14 with Mathematics categories.

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.

Semilinear Evolution Equations And Their Applications

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Author : Toka Diagana
language : en
Publisher: Springer
Release Date : 2018-10-23

Semilinear Evolution Equations And Their Applications written by Toka Diagana and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-10-23 with Mathematics categories.

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.

Abstract Cauchy Problems And Functional Differential Equations

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Author : F. Kappel
language : en
Publisher: Pitman Publishing
Release Date : 1981

Abstract Cauchy Problems And Functional Differential Equations written by F. Kappel and has been published by Pitman Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 1981 with Mathematics categories.

Applied Nonlinear Semigroups

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Author : A. Belleni-Morante
language : en
Publisher: John Wiley & Sons
Release Date : 1998-12-04

Applied Nonlinear Semigroups written by A. Belleni-Morante and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-12-04 with Mathematics categories.

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.

Attractors Shadowing And Approximation Of Abstract Semilinear Differential Equations

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Author : Sergey I Piskarev
language : en
Publisher: World Scientific
Release Date : 2023-07-05

Attractors Shadowing And Approximation Of Abstract Semilinear Differential Equations written by Sergey I Piskarev and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-07-05 with Mathematics categories.

The book is devoted to some branches of the theory of approximation of abstract differential equations, namely, approximation of attractors in the case of hyperbolic equilibrium points, shadowing, and approximation of time-fractional semilinear problems.In this book, the most famous methods of several urgent branches of the theory of abstract differential equations scattered in numerous journal publications are systematized and collected together, which makes it convenient for the initial study of the subject and also for its use as a reference book. The presentation of the material is closed and accompanied by examples; this makes it easier to understand the material and helps beginners to quickly enter into the circle of ideas discussed.The book can be useful for specialists in partial differential equations, functional analysis, theory of approximation of differential equations, and for all researchers, students, and postgraduates who apply these branches of mathematics in their work.

Mathematical Modeling And Control In Life And Environmental Sciences

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Author : Sebastian Aniţa
language : en
Publisher: Springer Nature
Release Date :

Mathematical Modeling And Control In Life And Environmental Sciences written by Sebastian Aniţa and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.