Existence Families Functional Calculi And Evolution Equations

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Existence Families, Functional Calculi and Evolution Equations

Ralph DeLaubenfels
Existence Families Functional Calculi and Evolution Equations Book PDF

Author : Ralph DeLaubenfels
Publisher : Springer
Page : 254 pages
File Size : 41,6 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540483229

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Existence Families, Functional Calculi and Evolution Equations by Ralph DeLaubenfels Pdf

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.

From Divergent Power Series to Analytic Functions

Werner Balser
From Divergent Power Series to Analytic Functions Book PDF

Author : Werner Balser
Publisher : Springer
Page : 124 pages
File Size : 45,5 Mb
Release : 1994-08-29
Category : Mathematics
ISBN : 3540582681

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From Divergent Power Series to Analytic Functions by Werner Balser Pdf

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.

Functional Analytic Methods for Evolution Equations

Giuseppe Da Prato,Peer Christian Kunstmann,Irena Lasiecka,Alessandra Lunardi,Roland Schnaubelt,Lutz Weis
Functional Analytic Methods for Evolution Equations Book PDF

Author : Giuseppe Da Prato,Peer Christian Kunstmann,Irena Lasiecka,Alessandra Lunardi,Roland Schnaubelt,Lutz Weis
Publisher : Springer Science & Business Media
Page : 486 pages
File Size : 48,6 Mb
Release : 2004-09-22
Category : Mathematics
ISBN : 3540230300

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Functional Analytic Methods for Evolution Equations by Giuseppe Da Prato,Peer Christian Kunstmann,Irena Lasiecka,Alessandra Lunardi,Roland Schnaubelt,Lutz Weis Pdf

This book consists of five introductory contributions by leading mathematicians on the functional analytic treatment of evolutions equations. In particular the contributions deal with Markov semigroups, maximal L^p-regularity, optimal control problems for boundary and point control systems, parabolic moving boundary problems and parabolic nonautonomous evolution equations. The book is addressed to PhD students, young researchers and mathematicians doing research in one of the above topics.

Fractional Evolution Equations and Inclusions

Yong Zhou
Fractional Evolution Equations and Inclusions Book PDF

Author : Yong Zhou
Publisher : Academic Press
Page : 294 pages
File Size : 51,6 Mb
Release : 2016-02-05
Category : Mathematics
ISBN : 9780128047750

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Fractional Evolution Equations and Inclusions by Yong Zhou Pdf

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

Basic Theory Of Fractional Differential Equations (Third Edition)

Yong Zhou
Basic Theory Of Fractional Differential Equations Third Edition Book PDF

Author : Yong Zhou
Publisher : World Scientific
Page : 516 pages
File Size : 45,9 Mb
Release : 2023-10-06
Category : Mathematics
ISBN : 9789811271700

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Basic Theory Of Fractional Differential Equations (Third Edition) by Yong Zhou Pdf

This accessible monograph is devoted to a rapidly developing area on the research of qualitative theory of fractional ordinary differential equations and evolution equations. It is self-contained and unified in presentation, and provides the readers the necessary background material required to go further into the subject and explore the rich research literature. The tools used include many classical and modern nonlinear analysis methods such as fixed point theory, measure of noncompactness method, topological degree method, Picard operators technique, critical point theory and semigroups theory. This book is based on the research work done so far by the author and other experts, and contains comprehensive up-to-date materials on the topic.In this third edition, four new topics have been added: Hilfer fractional evolution equations and infinite interval problems, oscillations and nonoscillations, fractional Hamiltonian systems, fractional Rayleigh-Stokes equations, and wave equations. The bibliography has also been updated and expanded.This book is useful to researchers, graduate or PhD students dealing with fractional calculus and applied analysis, differential equations, and related areas of research.

Recent Developments in Evolution Equations

G F Roach,A C Mcbride
Recent Developments in Evolution Equations Book PDF

Author : G F Roach,A C Mcbride
Publisher : CRC Press
Page : 268 pages
File Size : 54,9 Mb
Release : 1995-04-28
Category : Mathematics
ISBN : 0582246695

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Recent Developments in Evolution Equations by G F Roach,A C Mcbride Pdf

This book presents the majority of talks given at an International Converence held recently at the University of Strathclyde in Glasgow. The works presented focus on the analysis of mathematical models of systems evolving with time. The main topics are semigroups and related subjects connected with applications to partial differential equations of evolution type. Topics of particular interest include spectral and asymptotic properties of semigroups, B evolution scattering theory, and coagulation fragmentation phenomena.

Evolution Equations

Guillermo Segundo Ferreyra,Gisèle Ruiz Goldstein,Frank Neubrander
Evolution Equations Book PDF

Author : Guillermo Segundo Ferreyra,Gisèle Ruiz Goldstein,Frank Neubrander
Publisher : CRC Press
Page : 468 pages
File Size : 50,7 Mb
Release : 1994-10-20
Category : Mathematics
ISBN : 0824792874

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Evolution Equations by Guillermo Segundo Ferreyra,Gisèle Ruiz Goldstein,Frank Neubrander Pdf

Based on the lnternational Conference on Evolution Equations held recently at Louisiana State University, Baton Rouge, this work presents significant new research papers and state-of-the-art surveys on evolution equations and related fields. Important applications of evolution equations to problems in quantum theory, fluid dynamics, engineering, and biology are highlighted.

Almost Periodic and Almost Automorphic Solutions to Integro-Differential Equations

Marko Kostić
Almost Periodic and Almost Automorphic Solutions to Integro Differential Equations Book PDF

Author : Marko Kostić
Publisher : Walter de Gruyter GmbH & Co KG
Page : 372 pages
File Size : 49,8 Mb
Release : 2019-05-06
Category : Mathematics
ISBN : 9783110641851

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Almost Periodic and Almost Automorphic Solutions to Integro-Differential Equations by Marko Kostić Pdf

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.

Semigroups of Operators: Theory and Applications

A.V. Balakrishnan
Semigroups of Operators Theory and Applications Book PDF

Author : A.V. Balakrishnan
Publisher : Birkhäuser
Page : 376 pages
File Size : 46,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034884174

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Semigroups of Operators: Theory and Applications by A.V. Balakrishnan Pdf

These Proceedings comprise the bulk of the papers presented at the Inter national Conference on Semigroups of Opemtors: Theory and Contro~ held 14-18 December 1998, Newport Beach, California, U.S.A. The intent of the Conference was to highlight recent advances in the the ory of Semigroups of Operators which provides the abstract framework for the time-domain solutions of time-invariant boundary-value/initial-value problems of partial differential equations. There is of course a firewall between the ab stract theory and the applications and one of the Conference aims was to bring together both in the hope that it may be of value to both communities. In these days when all scientific activity is judged by its value on "dot com" it is not surprising that mathematical analysis that holds no promise of an immediate commercial product-line, or even a software tool-box, is not high in research priority. We are particularly pleased therefore that the National Science Foundation provided generous financial support without which this Conference would have been impossible to organize. Our special thanks to Dr. Kishan Baheti, Program Manager.

Beyond Partial Differential Equations

Horst Reinhard Beyer
Beyond Partial Differential Equations Book PDF

Author : Horst Reinhard Beyer
Publisher : Springer
Page : 291 pages
File Size : 47,7 Mb
Release : 2007-04-10
Category : Mathematics
ISBN : 9783540711292

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Beyond Partial Differential Equations by Horst Reinhard Beyer Pdf

This book introduces the treatment of linear and nonlinear (quasi-linear) abstract evolution equations by methods from the theory of strongly continuous semigroups. The theoretical part is accessible to graduate students with basic knowledge in functional analysis, with only some examples requiring more specialized knowledge from the spectral theory of linear, self-adjoint operators in Hilbert spaces. Emphasis is placed on equations of the hyperbolic type which are less often treated in the literature.

Perspectives in Mathematical Sciences

Yisong Yang,Jinqiao Duan,Xinchu Fu
Perspectives in Mathematical Sciences Book PDF

Author : Yisong Yang,Jinqiao Duan,Xinchu Fu
Publisher : World Scientific
Page : 371 pages
File Size : 46,7 Mb
Release : 2010
Category : Mathematics
ISBN : 9789814289313

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Perspectives in Mathematical Sciences by Yisong Yang,Jinqiao Duan,Xinchu Fu Pdf

1. Periodic boundary problems for analytic function including automorphic functions / Haitao Cai and Jian-Ke Lu -- 2. Subharmonic bifurcations and chaos for a model of micro-cantilever in MEMS / Yushu Chen, Liangqiang Zhou and Fangqi Chen -- 3. Canonical sample spaces for random dynamical systems / Jinqiao Duan, Xingye Kan and Bjorn Schmalfuss -- 4. Epidemic propagation dynamics on complex networks / Xinchu Fu ... [et al.] -- 5. Inverse problems for equations of parabolic type / Zhibin Han, Yongzhong Huang and Ming Jian -- 6. The existence and asymptotic properties of nontrivial solutions of nonlinear (2 - q)-Laplacian type problems with linking geometric structure / Gongbao Li and Zhaofen Shen -- 7. Chaotic dynamics for the two-component Bose-Einstein condensate system / Jibin Li -- 8. Recent developments and perspectives in nonlinear dynamics / Zengrong Liu -- 9. Mathematical aspects of the cold plasma model / Thomas H. Otway -- 10. Gravitating Yang-Mills fields in all dimensions / Eugen Radu and D. H. Tchrakian -- 11. Hamiltonian constraint and Mandelstam identities over extended knot families [symbol] and [symbol] in extended loop gravity / Dan Shao, Liang Shao and Changgui Shao -- 12. Lattice Boltzmann simulation of nonlinear Schrödinger equation with variable coefficients / Baochang Shi -- 13. Exponential stability of nonlocal time-delayed burgers equation / Yanbin Tang -- 14. Bifurcation analysis of the Swift-Hohenberg equation with quintic nonlinearity and Neumann boundary condition / Qingkun Xiao and Hongjun Gao -- 15. A new GL method for mathematical and physical problems / Ganquan Xie and Jianhua Li -- 16. Harmonically representing topological classes / Yisong Yang.

Nonlinear Partial Differential Equations and Applications

Boling Guo,Dadi Yang
Nonlinear Partial Differential Equations and Applications Book PDF

Author : Boling Guo,Dadi Yang
Publisher : World Scientific
Page : 268 pages
File Size : 51,9 Mb
Release : 1998-10-30
Category : Electronic
ISBN : 9789814544269

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Nonlinear Partial Differential Equations and Applications by Boling Guo,Dadi Yang Pdf

Contents: Direct and Inverse Diffraction by Periodic Structures (G Bao)Weak Flow of H-Systems (Y-M Chen)Strongly Compact Attractor for Dissipative Zakharov Equations (B-L Guo et al.)C∞-Solutions of Generalized Porous Medium Equations (M Ôtani & Y Sugiyama)Cauchy Problem for Generalized IMBq Equation (G-W Chen & S-B Wang)Inertial Manifolds for a Nonlocal Kuramoto–Sivashinsky Equation (J-Q Duan et al.)Weak Solutions of the Generalized Magnetic Flow Equations (S-H He & Z-D Dai)The Solution of Hammerstein Integral Equation Without Coercive Conditions (Y-L Shu)Global Behaviour of the Solution of Nonlinear Forest Evolution Equation (D-J Wang)Uniqueness of Generalized Solutions for Semiconductor Equations (J-S Xing & Y Hu)On the Vectorial Hamilton–Jacobi System (B-S Yan)An Integrable Hamiltonian System Associated with cKdV Hierarchy (J-S Zhang et al.)and other papers Readership: Mathematicians. Keywords:Diffraction;Weak Flow;Zakharov Equations;Porous Medium Equations;Cauchy Problem;IMBq Equation;Kuramoto-Sivashinsky Equation;Magnetic Flow Equations;Hammerstein Integral Equation;Nonlinear Forest Evolution Equation;Uniqueness;Generalized Solutions;Semiconductor Equations;Hamilton–Jacobi System;Hamiltonian System;cKdV Hierarchy

Geometric Aspects of Functional Analysis

V.D. Milman,G. Schechtman
Geometric Aspects of Functional Analysis Book PDF

Author : V.D. Milman,G. Schechtman
Publisher : Springer
Page : 296 pages
File Size : 55,8 Mb
Release : 2007-05-09
Category : Mathematics
ISBN : 9783540453925

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Geometric Aspects of Functional Analysis by V.D. Milman,G. Schechtman Pdf

This volume of original research papers from the Israeli GAFA seminar during the years 1996-2000 not only reports on more traditional directions of Geometric Functional Analysis, but also reflects on some of the recent new trends in Banach Space Theory and related topics. These include the tighter connection with convexity and the resulting added emphasis on convex bodies that are not necessarily centrally symmetric, and the treatment of bodies which have only very weak convex-like structure. Another topic represented here is the use of new probabilistic tools; in particular transportation of measure methods and new inequalities emerging from Poincaré-like inequalities.

A Short Course on Operator Semigroups

Klaus-Jochen Engel,Rainer Nagel
A Short Course on Operator Semigroups Book PDF

Author : Klaus-Jochen Engel,Rainer Nagel
Publisher : Springer Science & Business Media
Page : 257 pages
File Size : 49,8 Mb
Release : 2006-10-14
Category : Mathematics
ISBN : 9780387366197

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A Short Course on Operator Semigroups by Klaus-Jochen Engel,Rainer Nagel Pdf

The book offers a direct and up-to-date introduction to the theory of one-parameter semigroups of linear operators on Banach spaces. It contains the fundamental results of the theory such as the Hille-Yoshida generation theorem, the bounded perturbation theorem, and the Trotter-Kato approximation theorem. It also treats the spectral theory of semigroups and its consequences for the qualitative behavior. The book is intended for students and researchers who want to become acquainted with the concept of semigroups in order to work with it in fields like partial and functional differential equations. Exercises are provided at the end of the chapters.

Nonlinear Dynamics and Pattern Formation in the Natural Environment

A. Van Harten,A. Doelman
Nonlinear Dynamics and Pattern Formation in the Natural Environment Book PDF

Author : A. Van Harten,A. Doelman
Publisher : Taylor & Francis
Page : 344 pages
File Size : 42,8 Mb
Release : 2022-09-16
Category : Mathematics
ISBN : 9781351428279

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Nonlinear Dynamics and Pattern Formation in the Natural Environment by A. Van Harten,A. Doelman Pdf

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.