Existence Families Functional Calculi And Evolution Equations
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Existence Families Functional Calculi And Evolution Equations
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Author : Ralph DeLaubenfels
language : en
Publisher: Springer
Release Date : 2006-11-15
Existence Families Functional Calculi And Evolution Equations written by Ralph DeLaubenfels and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.
This book presents an operator-theoretic approach to ill-posed evolution equations. It presents the basic theory, and the more surprising examples, of generalizations of strongly continuous semigroups known as 'existent families' and 'regularized semigroups'. These families of operators may be used either to produce all initial data for which a solution in the original space exists, or to construct a maximal subspace on which the problem is well-posed. Regularized semigroups are also used to construct functional, or operational, calculi for unbounded operators. The book takes an intuitive and constructive approach by emphasizing the interaction between functional calculus constructions and evolution equations. One thinks of a semigroup generated by A as etA and thinks of a regularized semigroup generated by A as etA g(A), producing solutions of the abstract Cauchy problem for initial data in the image of g(A). Material that is scattered throughout numerous papers is brought together and presented in a fresh, organized way, together with a great deal of new material.
Existence Families Functional Calculi And Evolution Equations
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Author : Ralph Delaubenfels
language : en
Publisher:
Release Date : 2014-01-15
Existence Families Functional Calculi And Evolution Equations written by Ralph Delaubenfels and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.
From Divergent Power Series To Analytic Functions
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Author : Werner Balser
language : en
Publisher: Springer
Release Date : 1994-08-29
From Divergent Power Series To Analytic Functions written by Werner Balser and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-08-29 with Mathematics categories.
Multisummability is a method which, for certain formal power series with radius of convergence equal to zero, produces an analytic function having the formal series as its asymptotic expansion. This book presents the theory of multisummabi- lity, and as an application, contains a proof of the fact that all formal power series solutions of non-linear meromorphic ODE are multisummable. It will be of use to graduate students and researchers in mathematics and theoretical physics, and especially to those who encounter formal power series to (physical) equations with rapidly, but regularly, growing coefficients.
Fractional Evolution Equations And Inclusions
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Author : Yong Zhou
language : en
Publisher: Academic Press
Release Date : 2016-02-05
Fractional Evolution Equations And Inclusions written by Yong Zhou and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-02-05 with Mathematics categories.
Fractional evolution inclusions are an important form of differential inclusions within nonlinear mathematical analysis. They are generalizations of the much more widely developed fractional evolution equations (such as time-fractional diffusion equations) seen through the lens of multivariate analysis. Compared to fractional evolution equations, research on the theory of fractional differential inclusions is however only in its initial stage of development. This is important because differential models with the fractional derivative providing an excellent instrument for the description of memory and hereditary properties, and have recently been proved valuable tools in the modeling of many physical phenomena. The fractional order models of real systems are always more adequate than the classical integer order models, since the description of some systems is more accurate when the fractional derivative is used. The advantages of fractional derivatization become evident in modeling mechanical and electrical properties of real materials, description of rheological properties of rocks and in various other fields. Such models are interesting for engineers and physicists as well as so-called pure mathematicians. Phenomena investigated in hybrid systems with dry friction, processes of controlled heat transfer, obstacle problems and others can be described with the help of various differential inclusions, both linear and nonlinear. Fractional Evolution Equations and Inclusions is devoted to a rapidly developing area of the research for fractional evolution equations & inclusions and their applications to control theory. It studies Cauchy problems for fractional evolution equations, and fractional evolution inclusions with Hille-Yosida operators. It discusses control problems for systems governed by fractional evolution equations. Finally it provides an investigation of fractional stochastic evolution inclusions in Hilbert spaces. - Systematic analysis of existence theory and topological structure of solution sets for fractional evolution inclusions and control systems - Differential models with fractional derivative provide an excellent instrument for the description of memory and hereditary properties, and their description and working will provide valuable insights into the modelling of many physical phenomena suitable for engineers and physicists - The book provides the necessary background material required to go further into the subject and explore the rich research literature
Evolution Semigroups In Dynamical Systems And Differential Equations
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Author : Carmen Chicone
language : en
Publisher: American Mathematical Soc.
Release Date : 1999
Evolution Semigroups In Dynamical Systems And Differential Equations written by Carmen Chicone 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 1999 with Mathematics categories.
The main theme of the book is the spectral theory for evolution operators and evolution semigroups, a subject tracing its origins to the classical results of J. Mather on hyperbolic dynamical systems and J. Howland on nonautonomous Cauchy problems. The authors use a wide range of methods and offer a unique presentation. The authors give a unifying approach for a study of infinite-dimensional nonautonomous problems, which is based on the consistent use of evolution semigroups. This unifying idea connects various questions in stability of semigroups, infinite-dimensional hyperbolic linear skew-product flows, translation Banach algebras, transfer operators, stability radii in control theory, Lyapunov exponents, magneto-dynamics and hydro-dynamics. Thus the book is much broader in scope than existing books on asymptotic behavior of semigroups. Included is a solid collection of examples from different areas of analysis, PDEs, and dynamical systems. This is the first monograph where the spectral theory of infinite dimensional linear skew-product flows is described together with its connection to the multiplicative ergodic theorem; the same technique is used to study evolution semigroups, kinematic dynamos, and Ruelle operators; the theory of stability radii, an important concept in control theory, is also presented. Examples are included and non-traditional applications are provided.
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 Volterra Integro Differential Equations
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Author : Marko Kostic
language : en
Publisher: CRC Press
Release Date : 2015-05-06
Abstract Volterra Integro Differential Equations written by Marko Kostic and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-05-06 with Mathematics categories.
The theory of linear Volterra integro-differential equations has been developing rapidly in the last three decades. This book provides an easy to read concise introduction to the theory of ill-posed abstract Volterra integro-differential equations. A major part of the research is devoted to the study of various types of abstract (multi-term) fracti
Finsler Metrics A Global Approach
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Author : Marco Abate
language : en
Publisher: Springer
Release Date : 2006-11-15
Finsler Metrics A Global Approach written by Marco Abate and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.
Complex Finsler metrics appear naturally in complex analysis. To develop new tools in this area, the book provides a graduate-level introduction to differential geometry of complex Finsler metrics. After reviewing real Finsler geometry stressing global results, complex Finsler geometry is presented introducing connections, Kählerianity, geodesics, curvature. Finally global geometry and complex Monge-Ampère equations are discussed for Finsler manifolds with constant holomorphic curvature, which are important in geometric function theory. Following E. Cartan, S.S. Chern and S. Kobayashi, the global approach carries the full strength of hermitian geometry of vector bundles avoiding cumbersome computations, and thus fosters applications in other fields.
Nonlinear Dynamics And Pattern Formation In The Natural Environment
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Author : A Doelman
language : en
Publisher: Taylor & Francis
Release Date : 2022-09-16
Nonlinear Dynamics And Pattern Formation In The Natural Environment written by A Doelman and has been published by Taylor & Francis this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-09-16 with Mathematics categories.
This Research Note aims to provide an insight into recent developments in the theory of pattern formation. In the last decade there has been considerable progress in this field, both from a theoretical and a practical point of view. Recent mathematical developments concern the study of the nonlinear stability of systems at near-critical conditions by an appropriate system of modulation equations. The complexity of the original problem can be reduced drastically by this approximation. Moreover, it provides unifying point of view for a wide range of problems. New applications of the theory arise in a multitude of scientific areas such as hydrodynamics, reaction-diffusion problems, oceanography, meteorology, combustion, geophysical and biological morphodynamics and semi-conductors.This book is intended to show the interactions between the mathematical theory of nonlinear dynamics and the study of pattern generating phenomena in the natural environment. There is an intimate relationship between new insights in the mathematical aspects of nonlinear pattern formation and the comprehension of such phenomena. Therefore there are two partly overlapping main themes: one in which the emphasis is on generally applicable mathematical theories and techniques and one in which the phenomenology of pattern evolution in various areas is discussed.The book comprises 19 contributions by experts in the field. Although the emphasis changes considerably from paper to paper, in each contribution the same two themes are present; all the authors have aimed to achieve a suitable balance between the mathematical theory and the physical phenomena.
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.