Linear And Quasilinear 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.
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.
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.
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.
Pseudo Differential Operators And Markov Processes Volume Ii Generators And Their Potential Theory
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Author : Niels Jacob
language : en
Publisher: World Scientific
Release Date : 2002-07-19
Pseudo Differential Operators And Markov Processes Volume Ii Generators And Their Potential Theory written by Niels Jacob and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-07-19 with Mathematics categories.
In this volume two topics are discussed: the construction of Feller and Lp-sub-Markovian semigroups by starting with a pseudo-differential operator, and the potential theory of these semigroups and their generators. The first part of the text essentially discusses the analysis of pseudo-differential operators with negative definite symbols and develops a symbolic calculus; in addition, it deals with special approaches, such as subordination in the sense of Bochner. The second part handles capacities, function spaces associated with continuous negative definite functions, Lp -sub-Markovian semigroups in their associated Bessel potential spaces, Stein's Littlewood-Paley theory, global properties of Lp-sub-Markovian semigroups, and estimates for transition functions.
Calculus Of Variations And Partial Differential Equations
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Author : Stefan Hildebrandt
language : en
Publisher: Springer
Release Date : 2006-11-14
Calculus Of Variations And Partial Differential Equations written by Stefan Hildebrandt and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.
Abstract Parabolic Evolution Equations And Their Applications
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Author : Atsushi Yagi
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-11-03
Abstract Parabolic Evolution Equations And Their Applications written by Atsushi Yagi 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 2009-11-03 with Mathematics categories.
This monograph is intended to present the fundamentals of the theory of abstract parabolic evolution equations and to show how to apply to various nonlinear dif- sion equations and systems arising in science. The theory gives us a uni?ed and s- tematic treatment for concrete nonlinear diffusion models. Three main approaches are known to the abstract parabolic evolution equations, namely, the semigroup methods, the variational methods, and the methods of using operational equations. In order to keep the volume of the monograph in reasonable length, we will focus on the semigroup methods. For other two approaches, see the related references in Bibliography. The semigroup methods, which go back to the invention of the analytic se- groups in the middle of the last century, are characterized by precise formulas representing the solutions of the Cauchy problem for evolution equations. The ?tA analytic semigroup e generated by a linear operator ?A provides directly a fundamental solution to the Cauchy problem for an autonomous linear e- dU lution equation, +AU =F(t), 0
Mathematical Reviews
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Author :
language : en
Publisher:
Release Date : 2007
Mathematical Reviews written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.
A Theory Of Optimization And Optimal Control For Nonlinear Evolution And Singular Equations
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Author : Mieczyslaw Altman
language : en
Publisher: World Scientific
Release Date : 1990
A Theory Of Optimization And Optimal Control For Nonlinear Evolution And Singular Equations written by Mieczyslaw Altman and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with Science categories.
This research monograph offers a general theory which encompasses almost all known general theories in such a way that many practical applications can be obtained. It will be useful for mathematicians interested in the development of the abstract Control Theory with applications to Nonlinear PDE, as well as physicists, engineers, and economists looking for theoretical guidance in solving their optimal control problems; and graduate-level seminar courses in nonlinear applied functional analysis.
Moving Interfaces And Quasilinear Parabolic Evolution Equations
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Author : Jan Prüss
language : en
Publisher: Birkhäuser
Release Date : 2016-07-25
Moving Interfaces And Quasilinear Parabolic Evolution Equations written by Jan Prüss and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-07-25 with Mathematics categories.
In this monograph, the authors develop a comprehensive approach for the mathematical analysis of a wide array of problems involving moving interfaces. It includes an in-depth study of abstract quasilinear parabolic evolution equations, elliptic and parabolic boundary value problems, transmission problems, one- and two-phase Stokes problems, and the equations of incompressible viscous one- and two-phase fluid flows. The theory of maximal regularity, an essential element, is also fully developed. The authors present a modern approach based on powerful tools in classical analysis, functional analysis, and vector-valued harmonic analysis. The theory is applied to problems in two-phase fluid dynamics and phase transitions, one-phase generalized Newtonian fluids, nematic liquid crystal flows, Maxwell-Stefan diffusion, and a variety of geometric evolution equations. The book also includes a discussion of the underlying physical and thermodynamic principles governing the equations of fluid flows and phase transitions, and an exposition of the geometry of moving hypersurfaces.