Evolution Equations In Scales Of Banach Spaces

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Evolution Equations In Scales Of Banach Spaces

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Author : Oliver Caps
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Evolution Equations In Scales Of Banach Spaces written by Oliver Caps 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 2012-12-06 with Mathematics categories.

The book provides a new functional-analytic approach to evolution equations by considering the abstract Cauchy problem in a scale of Banach spaces. The usual functional analytic methods for studying evolution equations are formu lated within the setting of unbounded, closed operators in one Banach space. This setting is not adapted very well to the study of many pseudo differential and differential equations because these operators are naturally not given as closed, unbounded operators in one Banach space but as continuous opera tors in a scale of function spaces. Thus, applications within the setting of unbounded, closed operators require a considerable amount of additional work because one has to construct suitable closed realizations of these operators. This choice of closed realizations is technically complicated even for simple applications. The main feature of the new functional analytic approach of the book is to study the operators in scales of Banach spaces that are constructed by simple reference operators. This is a natural setting for many operators acting in scales of function spaces. The operators are only expected to respect the scale and to satisfy certain inequalities but we can avoid completely the choice of any closed realization of these operators which is of great importance in applications. We use the mapping properties of the reference operators to prove sufficient conditions for well-posedness of linear and quasilinear Cauchy problems. In the linear, time-dependent case these conditions are shown to characterize well-posedness. A similar result in the standard setting (i. e.

Evolution Equations And Scales Of Banach Spaces

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Author : Gui-Zhong Liu
language : en
Publisher:
Release Date : 1989

Evolution Equations And Scales Of Banach Spaces written by Gui-Zhong Liu and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with Semigroups of operators categories.

Linear And Quasilinear Parabolic Problems

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Author : Herbert Amann
language : en
Publisher: Springer Science & Business Media
Release Date : 1995

Linear And Quasilinear Parabolic Problems written by Herbert Amann 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 1995 with Differential equations, Parabolic categories.

Linear And Quasilinear Evolution Equations In Scales Of Banach Spaces

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Author : Oliver Caps
language : en
Publisher:
Release Date : 2000

Linear And Quasilinear Evolution Equations In Scales Of Banach Spaces written by Oliver Caps and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with categories.

Evolution Equations Semigroups And Functional Analysis

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Author : Alfredo Lorenzi
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06

Evolution Equations Semigroups And Functional Analysis written by Alfredo Lorenzi and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

Brunello Terreni (1953-2000) was a researcher and teacher with vision and dedication. The present volume is dedicated to the memory of Brunello Terreni. His mathematical interests are reflected in 20 expository articles written by distinguished mathematicians. The unifying theme of the articles is "evolution equations and functional analysis", which is presented in various and diverse forms: parabolic equations, semigroups, stochastic evolution, optimal control, existence, uniqueness and regularity of solutions, inverse problems as well as applications. Contributors: P. Acquistapace, V. Barbu, A. Briani, L. Boccardo, P. Colli Franzone, G. Da Prato, D. Donatelli, A. Favini, M. Fuhrmann, M. Grasselli, R. Illner, H. Koch, R. Labbas, H. Lange, I. Lasiecka, A. Lorenzi, A. Lunardi, P. Marcati, R. Nagel, G. Nickel, V. Pata, M. M. Porzio, B. Ruf, G. Savaré, R. Schnaubelt, E. Sinestrari, H. Tanabe, H. Teismann, E. Terraneo, R. Triggiani, A. Yagi.

Averaged Evolution Equations

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Author : Alberto Arosio
language : de
Publisher:
Release Date : 1995

Averaged Evolution Equations written by Alberto Arosio and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with categories.

A Unified Theory Of Nonlinear Operator And Evolution Equations With Applications

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Author : Mieczyslaw Altman
language : en
Publisher:
Release Date : 1986

A Unified Theory Of Nonlinear Operator And Evolution Equations With Applications written by Mieczyslaw Altman and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986 with Mathematics categories.

Functional Analytic Methods In Complex Analysis And Applications To Partial Differential Equations

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Author : A S A Mshimba
language : en
Publisher: World Scientific
Release Date : 1995-10-17

Functional Analytic Methods In Complex Analysis And Applications To Partial Differential Equations written by A S A Mshimba and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-10-17 with categories.

These proceedings concentrate on recent results in the following fields of complex analysis: complex methods for solving boundary value problems with piecewise smooth boundary data, complex methods for linear and nonlinear differential equations and systems of second order, and applications of scales of Banach spaces to initial value problems.Some problems in higher dimensions (such as the unification of global and local existence theorems for holomorphic functions and an elementary approach to Clifford analysis) are also discussed.Particular emphasis is placed on Symbolic Computation in Complex Analysis and on the new approaches to teach mathematical analysis based on interactions between complex analysis and partial differential equations.

Studies In Evolution Equations And Related Topics

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Author : Gaston M. N'Guérékata
language : en
Publisher: Springer Nature
Release Date : 2021-10-27

Studies In Evolution Equations And Related Topics written by Gaston M. N'Guérékata and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-10-27 with Mathematics categories.

This volume features recent development and techniques in evolution equations by renown experts in the field. Each contribution emphasizes the relevance and depth of this important area of mathematics and its expanding reach into the physical, biological, social, and computational sciences as well as into engineering and technology. The reader will find an accessible summary of a wide range of active research topics, along with exciting new results. Topics include: Impulsive implicit Caputo fractional q-difference equations in finite and infinite dimensional Banach spaces; optimal control of averaged state of a population dynamic model; structural stability of nonlinear elliptic p(u)-Laplacian problem with Robin-type boundary condition; exponential dichotomy and partial neutral functional differential equations, stable and center-stable manifolds of admissible class; global attractor in Alpha-norm for some partial functional differential equations of neutral and retarded type; and more. Researchers in mathematical sciences, biosciences, computational sciences and related fields, will benefit from the rich and useful resources provided. Upper undergraduate and graduate students may be inspired to contribute to this active and stimulating field.

Diagonalizing Quadratic Bosonic Operators By Non Autonomous Flow Equations

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Author : Volker Bach
language : en
Publisher: American Mathematical Soc.
Release Date : 2016-03-10

Diagonalizing Quadratic Bosonic Operators By Non Autonomous Flow Equations written by Volker Bach 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 2016-03-10 with Mathematics categories.

The authors study a non-autonomous, non-linear evolution equation on the space of operators on a complex Hilbert space. They specify assumptions that ensure the global existence of its solutions and allow them to derive its asymptotics at temporal infinity. They demonstrate that these assumptions are optimal in a suitable sense and more general than those used before. The evolution equation derives from the Brocket-Wegner flow that was proposed to diagonalize matrices and operators by a strongly continuous unitary flow. In fact, the solution of the non-linear flow equation leads to a diagonalization of Hamiltonian operators in boson quantum field theory which are quadratic in the field.