Phase Space Analysis Of Partial Differential Equations

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Phase Space Analysis Of Partial Differential Equations

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Author : Antonio Bove
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-12-28

Phase Space Analysis Of Partial Differential Equations written by Antonio Bove 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 2007-12-28 with Mathematics categories.

Covers phase space analysis methods, including microlocal analysis, and their applications to physics Treats the linear and nonnlinear aspects of the theory of PDEs Original articles are self-contained with full proofs; survey articles give a quick and direct introduction to selected topics evolving at a fast pace Excellent reference and resource for grad students and researchers in PDEs and related fields

Advances In Phase Space Analysis Of Partial Differential Equations

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Author : Antonio Bove
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-09-18

Advances In Phase Space Analysis Of Partial Differential Equations written by Antonio Bove 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 2009-09-18 with Mathematics categories.

This collection of original articles and surveys addresses the recent advances in linear and nonlinear aspects of the theory of partial differential equations. The key topics include operators as "sums of squares" of real and complex vector fields, nonlinear evolution equations, local solvability, and hyperbolic questions.

Phase Space Analysis Of Partial Differential Equations

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Author :
language : en
Publisher:
Release Date : 2004

Phase Space Analysis Of Partial Differential Equations written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with categories.

Studies In Phase Space Analysis With Applications To Pdes

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Author : Massimo Cicognani
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-12

Studies In Phase Space Analysis With Applications To Pdes written by Massimo Cicognani 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 2013-03-12 with Mathematics categories.

This collection of original articles and surveys, emerging from a 2011 conference in Bertinoro, Italy, addresses recent advances in linear and nonlinear aspects of the theory of partial differential equations (PDEs). Phase space analysis methods, also known as microlocal analysis, have continued to yield striking results over the past years and are now one of the main tools of investigation of PDEs. Their role in many applications to physics, including quantum and spectral theory, is equally important. Key topics addressed in this volume include: *general theory of pseudodifferential operators *Hardy-type inequalities *linear and non-linear hyperbolic equations and systems *Schrödinger equations *water-wave equations *Euler-Poisson systems *Navier-Stokes equations *heat and parabolic equations Various levels of graduate students, along with researchers in PDEs and related fields, will find this book to be an excellent resource. Contributors T. Alazard P.I. Naumkin J.-M. Bony F. Nicola N. Burq T. Nishitani C. Cazacu T. Okaji J.-Y. Chemin M. Paicu E. Cordero A. Parmeggiani R. Danchin V. Petkov I. Gallagher M. Reissig T. Gramchev L. Robbiano N. Hayashi L. Rodino J.Huang M. Ruzhanky D. Lannes J.-C. Saut F. Linares N. Visciglia P.B. Mucha P. Zhang C. Mullaert E. Zuazua T. Narazaki C. Zuily

Methods For Partial Differential Equations

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Author : Marcelo R. Ebert
language : en
Publisher: Birkhäuser
Release Date : 2018-03-06

Methods For Partial Differential Equations written by Marcelo R. Ebert and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-03-06 with Mathematics categories.

This book provides an overview of different topics related to the theory of partial differential equations. Selected exercises are included at the end of each chapter to prepare readers for the “research project for beginners” proposed at the end of the book. It is a valuable resource for advanced graduates and undergraduate students who are interested in specializing in this area. The book is organized in five parts: In Part 1 the authors review the basics and the mathematical prerequisites, presenting two of the most fundamental results in the theory of partial differential equations: the Cauchy-Kovalevskaja theorem and Holmgren's uniqueness theorem in its classical and abstract form. It also introduces the method of characteristics in detail and applies this method to the study of Burger's equation. Part 2 focuses on qualitative properties of solutions to basic partial differential equations, explaining the usual properties of solutions to elliptic, parabolic and hyperbolic equations for the archetypes Laplace equation, heat equation and wave equation as well as the different features of each theory. It also discusses the notion of energy of solutions, a highly effective tool for the treatment of non-stationary or evolution models and shows how to define energies for different models. Part 3 demonstrates how phase space analysis and interpolation techniques are used to prove decay estimates for solutions on and away from the conjugate line. It also examines how terms of lower order (mass or dissipation) or additional regularity of the data may influence expected results. Part 4 addresses semilinear models with power type non-linearity of source and absorbing type in order to determine critical exponents: two well-known critical exponents, the Fujita exponent and the Strauss exponent come into play. Depending on concrete models these critical exponents divide the range of admissible powers in classes which make it possible to prove quite different qualitative properties of solutions, for example, the stability of the zero solution or blow-up behavior of local (in time) solutions. The last part features selected research projects and general background material.

Metrics On The Phase Space And Non Selfadjoint Pseudo Differential Operators

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Author : Nicolas Lerner
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-01-30

Metrics On The Phase Space And Non Selfadjoint Pseudo Differential Operators written by Nicolas Lerner 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 2011-01-30 with Mathematics categories.

This book is devoted to the study of pseudo-di?erential operators, with special emphasis on non-selfadjoint operators, a priori estimates and localization in the phase space. We have tried here to expose the most recent developments of the theory with its applications to local solvability and semi-classical estimates for non-selfadjoint operators. The?rstchapter,Basic Notions of Phase Space Analysis,isintroductoryand gives a presentation of very classical classes of pseudo-di?erential operators, along with some basic properties. As an illustration of the power of these methods, we give a proof of propagation of singularities for real-principal type operators (using aprioriestimates,andnotFourierintegraloperators),andweintroducethereader to local solvability problems. That chapter should be useful for a reader, say at the graduate level in analysis, eager to learn some basics on pseudo-di?erential operators. The second chapter, Metrics on the Phase Space begins with a review of symplectic algebra, Wigner functions, quantization formulas, metaplectic group and is intended to set the basic study of the phase space. We move forward to the more general setting of metrics on the phase space, following essentially the basic assumptions of L. H ̈ ormander (Chapter 18 in the book [73]) on this topic.

Methods For Partial Differential Equations

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Author : Marcelo R. Ebert
language : en
Publisher: Birkhäuser
Release Date : 2018-02-23

Methods For Partial Differential Equations written by Marcelo R. Ebert and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-02-23 with Mathematics categories.

This book provides an overview of different topics related to the theory of partial differential equations. Selected exercises are included at the end of each chapter to prepare readers for the “research project for beginners” proposed at the end of the book. It is a valuable resource for advanced graduates and undergraduate students who are interested in specializing in this area. The book is organized in five parts: In Part 1 the authors review the basics and the mathematical prerequisites, presenting two of the most fundamental results in the theory of partial differential equations: the Cauchy-Kovalevskaja theorem and Holmgren's uniqueness theorem in its classical and abstract form. It also introduces the method of characteristics in detail and applies this method to the study of Burger's equation. Part 2 focuses on qualitative properties of solutions to basic partial differential equations, explaining the usual properties of solutions to elliptic, parabolic and hyperbolic equations for the archetypes Laplace equation, heat equation and wave equation as well as the different features of each theory. It also discusses the notion of energy of solutions, a highly effective tool for the treatment of non-stationary or evolution models and shows how to define energies for different models. Part 3 demonstrates how phase space analysis and interpolation techniques are used to prove decay estimates for solutions on and away from the conjugate line. It also examines how terms of lower order (mass or dissipation) or additional regularity of the data may influence expected results. Part 4 addresses semilinear models with power type non-linearity of source and absorbing type in order to determine critical exponents: two well-known critical exponents, the Fujita exponent and the Strauss exponent come into play. Depending on concrete models these critical exponents divide the range of admissible powers in classes which make it possible to prove quite different qualitative properties of solutions, for example, the stability of the zero solution or blow-up behavior of local (in time) solutions. The last part features selected research projects and general background material.

Pseudo Differential Operators Complex Analysis And Partial Differential Equations

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Author : Bert-Wolfgang Schulze
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-03-01

Pseudo Differential Operators Complex Analysis And Partial Differential Equations written by Bert-Wolfgang Schulze 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 2010-03-01 with Mathematics categories.

Consists of the expository paper based on the 6-hour minicourse given by Professor Bert-Wolfgang Schulze, and sixteen papers based on lectures given at the workshop and on invitations.

Partial Differential Equations

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Author : M. S. Agranovich
language : en
Publisher: American Mathematical Soc.
Release Date : 2002

Partial Differential Equations written by M. S. Agranovich 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 2002 with Mathematics categories.

This volume presents 11 papers from a Russian seminar on new developments in the study of both linear and nonlinear partial differential equations (PDEs). Topics include elliptic boundary value problems with large parameter for mixed order systems, a method of stabilization for solutions of the Navier-Stokes equations by a feedback control from the boundary, a class of dissipative nonlinear PDEs perturbed by a bounded random kick-force, and the stability of inverse problems. The last two chapters review the history of the Vishik seminar first held in 1961. There is no index. Annotation copyrighted by Book News, Inc., Portland, OR

Harmonic Analysis In Phase Space Am 122 Volume 122

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Author : Gerald B. Folland
language : en
Publisher: Princeton University Press
Release Date : 2016-03-02

Harmonic Analysis In Phase Space Am 122 Volume 122 written by Gerald B. Folland and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-03-02 with Mathematics categories.

This book provides the first coherent account of the area of analysis that involves the Heisenberg group, quantization, the Weyl calculus, the metaplectic representation, wave packets, and related concepts. This circle of ideas comes principally from mathematical physics, partial differential equations, and Fourier analysis, and it illuminates all these subjects. The principal features of the book are as follows: a thorough treatment of the representations of the Heisenberg group, their associated integral transforms, and the metaplectic representation; an exposition of the Weyl calculus of pseudodifferential operators, with emphasis on ideas coming from harmonic analysis and physics; a discussion of wave packet transforms and their applications; and a new development of Howe's theory of the oscillator semigroup.