Studies In Phase Space Analysis With Applications To Pdes

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Studies in Phase Space Analysis with Applications to PDEs

Massimo Cicognani,Ferruccio Colombini,Daniele Del Santo
Studies in Phase Space Analysis with Applications to PDEs Book PDF

Author : Massimo Cicognani,Ferruccio Colombini,Daniele Del Santo
Publisher : Springer Science & Business Media
Page : 391 pages
File Size : 53,9 Mb
Release : 2013-03-12
Category : Mathematics
ISBN : 9781461463481

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Studies in Phase Space Analysis with Applications to PDEs by Massimo Cicognani,Ferruccio Colombini,Daniele Del Santo Pdf

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

Marcelo R. Ebert,Michael Reissig
Methods for Partial Differential Equations Book PDF

Author : Marcelo R. Ebert,Michael Reissig
Publisher : Birkhäuser
Page : 456 pages
File Size : 41,9 Mb
Release : 2018-02-23
Category : Mathematics
ISBN : 9783319664569

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Methods for Partial Differential Equations by Marcelo R. Ebert,Michael Reissig Pdf

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.

Mathematical Analysis and Applications—Plenary Lectures

Luigi G. Rodino,Joachim Toft
Mathematical Analysis and Applications Plenary Lectures Book PDF

Author : Luigi G. Rodino,Joachim Toft
Publisher : Springer
Page : 207 pages
File Size : 50,8 Mb
Release : 2018-11-11
Category : Mathematics
ISBN : 9783030008741

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Mathematical Analysis and Applications—Plenary Lectures by Luigi G. Rodino,Joachim Toft Pdf

This book includes the texts of the survey lectures given by plenary speakers at the 11th International ISAAC Congress held in Växjö, Sweden, on 14-18 August, 2017. It is the purpose of ISAAC to promote analysis, its applications, and its interaction with computation. Analysis is understood here in the broad sense of the word, including differential equations, integral equations, functional analysis, and function theory. With this objective, ISAAC organizes international Congresses for the presentation and discussion of research on analysis. The plenary lectures in the present volume, authored by eminent specialists, are devoted to some exciting recent developments, topics including: local solvability for subprincipal type operators; fractional-order Laplacians; degenerate complex vector fields in the plane; lower bounds for pseudo-differential operators; a survey on Morrey spaces; localization operators in Signal Theory and Quantum Mechanics. Thanks to the accessible style used, readers only need a basic command of Calculus. This book will appeal to scientists, teachers, and graduate students in Mathematics, in particular Mathematical Analysis, Probability and Statistics, Numerical Analysis and Mathematical Physics.

New Tools for Nonlinear PDEs and Application

Marcello D'Abbicco,Marcelo Rempel Ebert,Vladimir Georgiev,Tohru Ozawa
New Tools for Nonlinear PDEs and Application Book PDF

Author : Marcello D'Abbicco,Marcelo Rempel Ebert,Vladimir Georgiev,Tohru Ozawa
Publisher : Springer
Page : 390 pages
File Size : 40,6 Mb
Release : 2019-05-07
Category : Mathematics
ISBN : 9783030109370

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New Tools for Nonlinear PDEs and Application by Marcello D'Abbicco,Marcelo Rempel Ebert,Vladimir Georgiev,Tohru Ozawa Pdf

This book features a collection of papers devoted to recent results in nonlinear partial differential equations and applications. It presents an excellent source of information on the state-of-the-art, new methods, and trends in this topic and related areas. Most of the contributors presented their work during the sessions "Recent progress in evolution equations" and "Nonlinear PDEs" at the 12th ISAAC congress held in 2017 in Växjö, Sweden. Even if inspired by this event, this book is not merely a collection of proceedings, but a stand-alone project gathering original contributions from active researchers on the latest trends in nonlinear evolution PDEs.

Partial Differential Equations arising from Physics and Geometry

Mohamed Ben Ayed,Mohamed Ali Jendoubi,Yomna Rébaï,Hasna Riahi,Hatem Zaag
Partial Differential Equations arising from Physics and Geometry Book PDF

Author : Mohamed Ben Ayed,Mohamed Ali Jendoubi,Yomna Rébaï,Hasna Riahi,Hatem Zaag
Publisher : Cambridge University Press
Page : 471 pages
File Size : 40,6 Mb
Release : 2019-05-02
Category : Mathematics
ISBN : 9781108431637

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Partial Differential Equations arising from Physics and Geometry by Mohamed Ben Ayed,Mohamed Ali Jendoubi,Yomna Rébaï,Hasna Riahi,Hatem Zaag Pdf

Presents the state of the art in PDEs, including the latest research and short courses accessible to graduate students.

Nonlinear PDEs: A Dynamical Systems Approach

Guido Schneider,Hannes Uecker
Nonlinear PDEs A Dynamical Systems Approach Book PDF

Author : Guido Schneider,Hannes Uecker
Publisher : American Mathematical Soc.
Page : 575 pages
File Size : 45,8 Mb
Release : 2017-10-26
Category : Differential equations, Nonlinear
ISBN : 9781470436131

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Nonlinear PDEs: A Dynamical Systems Approach by Guido Schneider,Hannes Uecker Pdf

This is an introductory textbook about nonlinear dynamics of PDEs, with a focus on problems over unbounded domains and modulation equations. The presentation is example-oriented, and new mathematical tools are developed step by step, giving insight into some important classes of nonlinear PDEs and nonlinear dynamics phenomena which may occur in PDEs. The book consists of four parts. Parts I and II are introductions to finite- and infinite-dimensional dynamics defined by ODEs and by PDEs over bounded domains, respectively, including the basics of bifurcation and attractor theory. Part III introduces PDEs on the real line, including the Korteweg-de Vries equation, the Nonlinear Schrödinger equation and the Ginzburg-Landau equation. These examples often occur as simplest possible models, namely as amplitude or modulation equations, for some real world phenomena such as nonlinear waves and pattern formation. Part IV explores in more detail the connections between such complicated physical systems and the reduced models. For many models, a mathematically rigorous justification by approximation results is given. The parts of the book are kept as self-contained as possible. The book is suitable for self-study, and there are various possibilities to build one- or two-semester courses from the book.

Cauchy Problem for Differential Operators with Double Characteristics

Tatsuo Nishitani
Cauchy Problem for Differential Operators with Double Characteristics Book PDF

Author : Tatsuo Nishitani
Publisher : Springer
Page : 213 pages
File Size : 44,9 Mb
Release : 2017-11-24
Category : Mathematics
ISBN : 9783319676128

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Cauchy Problem for Differential Operators with Double Characteristics by Tatsuo Nishitani Pdf

Combining geometrical and microlocal tools, this monograph gives detailed proofs of many well/ill-posed results related to the Cauchy problem for differential operators with non-effectively hyperbolic double characteristics. Previously scattered over numerous different publications, the results are presented from the viewpoint that the Hamilton map and the geometry of bicharacteristics completely characterizes the well/ill-posedness of the Cauchy problem. A doubly characteristic point of a differential operator P of order m (i.e. one where Pm = dPm = 0) is effectively hyperbolic if the Hamilton map FPm has real non-zero eigen values. When the characteristics are at most double and every double characteristic is effectively hyperbolic, the Cauchy problem for P can be solved for arbitrary lower order terms. If there is a non-effectively hyperbolic characteristic, solvability requires the subprincipal symbol of P to lie between −Pμj and Pμj , where iμj are the positive imaginary eigenvalues of FPm . Moreover, if 0 is an eigenvalue of FPm with corresponding 4 × 4 Jordan block, the spectral structure of FPm is insufficient to determine whether the Cauchy problem is well-posed and the behavior of bicharacteristics near the doubly characteristic manifold plays a crucial role.

Advances in Microlocal and Time-Frequency Analysis

Paolo Boggiatto,Marco Cappiello,Elena Cordero,Sandro Coriasco,Gianluca Garello,Alessandro Oliaro,Jörg Seiler
Advances in Microlocal and Time Frequency Analysis Book PDF

Author : Paolo Boggiatto,Marco Cappiello,Elena Cordero,Sandro Coriasco,Gianluca Garello,Alessandro Oliaro,Jörg Seiler
Publisher : Springer Nature
Page : 533 pages
File Size : 52,6 Mb
Release : 2020-03-03
Category : Mathematics
ISBN : 9783030361389

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Advances in Microlocal and Time-Frequency Analysis by Paolo Boggiatto,Marco Cappiello,Elena Cordero,Sandro Coriasco,Gianluca Garello,Alessandro Oliaro,Jörg Seiler Pdf

The present volume gathers contributions to the conference Microlocal and Time-Frequency Analysis 2018 (MLTFA18), which was held at Torino University from the 2nd to the 6th of July 2018. The event was organized in honor of Professor Luigi Rodino on the occasion of his 70th birthday. The conference’s focus and the contents of the papers reflect Luigi’s various research interests in the course of his long and extremely prolific career at Torino University.

Harmonic Analysis in Phase Space

G. B. Folland
Harmonic Analysis in Phase Space Book PDF

Author : G. B. Folland
Publisher : Princeton University Press
Page : 292 pages
File Size : 48,6 Mb
Release : 1989-03-21
Category : Mathematics
ISBN : 0691085285

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Harmonic Analysis in Phase Space by G. B. Folland Pdf

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.

Recent Trends in Operator Theory and Partial Differential Equations

Vladimir Maz'ya,David Natroshvili,Eugene Shargorodsky,Wolfgang L. Wendland
Recent Trends in Operator Theory and Partial Differential Equations Book PDF

Author : Vladimir Maz'ya,David Natroshvili,Eugene Shargorodsky,Wolfgang L. Wendland
Publisher : Birkhäuser
Page : 313 pages
File Size : 52,6 Mb
Release : 2017-02-23
Category : Mathematics
ISBN : 9783319470795

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Recent Trends in Operator Theory and Partial Differential Equations by Vladimir Maz'ya,David Natroshvili,Eugene Shargorodsky,Wolfgang L. Wendland Pdf

This volume is dedicated to the eminent Georgian mathematician Roland Duduchava on the occasion of his 70th birthday. It presents recent results on Toeplitz, Wiener-Hopf, and pseudodifferential operators, boundary value problems, operator theory, approximation theory, and reflects the broad spectrum of Roland Duduchava's research. The book is addressed to a wide audience of pure and applied mathematicians.

Fourier Analysis

Michael Ruzhansky,Ville Turunen
Fourier Analysis Book PDF

Author : Michael Ruzhansky,Ville Turunen
Publisher : Springer Science & Business Media
Page : 416 pages
File Size : 53,9 Mb
Release : 2014-01-18
Category : Mathematics
ISBN : 9783319025506

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Fourier Analysis by Michael Ruzhansky,Ville Turunen Pdf

This book is devoted to the broad field of Fourier analysis and its applications to several areas of mathematics, including problems in the theory of pseudo-differential operators, partial differential equations, and time-frequency analysis. It is based on lectures given at the international conference “Fourier Analysis and Pseudo-Differential Operators,” June 25–30, 2012, at Aalto University, Finland. This collection of 20 refereed articles is based on selected talks and presents the latest advances in the field. The conference was a satellite meeting of the 6th European Congress of Mathematics, which took place in Krakow in July 2012; it was also the 6th meeting in the series “Fourier Analysis and Partial Differential Equations.”

Microlocal Analysis, Sharp Spectral Asymptotics and Applications I

Victor Ivrii
Microlocal Analysis Sharp Spectral Asymptotics and Applications I Book PDF

Author : Victor Ivrii
Publisher : Springer Nature
Page : 889 pages
File Size : 52,6 Mb
Release : 2019-09-12
Category : Mathematics
ISBN : 9783030305574

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Microlocal Analysis, Sharp Spectral Asymptotics and Applications I by Victor Ivrii Pdf

The prime goal of this monograph, which comprises a total of five volumes, is to derive sharp spectral asymptotics for broad classes of partial differential operators using techniques from semiclassical microlocal analysis, in particular, propagation of singularities, and to subsequently use the variational estimates in “small” domains to consider domains with singularities of different kinds. In turn, the general theory (results and methods developed) is applied to the Magnetic Schrödinger operator, miscellaneous problems, and multiparticle quantum theory. In this volume the general microlocal semiclassical approach is developed, and microlocal and local semiclassical spectral asymptotics are derived.

Complex Analysis and Dynamical Systems VI: Part 1: PDE, Differential Geometry, Radon Transform

Matania Ben-Artzi, Greg Galloway,Lavi Karp,Dmitry Khavinson,Simeon Reich,Gilbert Weinstein,Lawrence Zalcman
Complex Analysis and Dynamical Systems VI Part 1 PDE Differential Geometry Radon Transform Book PDF

Author : Matania Ben-Artzi, Greg Galloway,Lavi Karp,Dmitry Khavinson,Simeon Reich,Gilbert Weinstein,Lawrence Zalcman
Publisher : American Mathematical Soc.
Page : 313 pages
File Size : 43,9 Mb
Release : 2015-12-03
Category : Calculus of variations
ISBN : 9781470416539

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Complex Analysis and Dynamical Systems VI: Part 1: PDE, Differential Geometry, Radon Transform by Matania Ben-Artzi, Greg Galloway,Lavi Karp,Dmitry Khavinson,Simeon Reich,Gilbert Weinstein,Lawrence Zalcman Pdf

This volume contains the proceedings of the Sixth International Conference on Complex Analysis and Dynamical Systems, held from May 19-24, 2013, in Nahariya, Israel, in honor of David Shoikhet's sixtieth birthday. The papers in this volume range over a wide variety of topics in Partial Differential Equations, Differential Geometry, and the Radon Transform. Taken together, the articles collected here provide the reader with a panorama of activity in partial differential equations and general relativity, drawn by a number of leading figures in the field. They testify to the continued vitality of the interplay between classical and modern analysis. The companion volume (Contemporary Mathematics, Volume 667) is devoted to complex analysis, quasiconformal mappings, and complex dynamics. This book is co-published with Bar-Ilan University (Ramat-Gan, Israel).

Microlocal Analysis, Sharp Spectral Asymptotics and Applications II

Victor Ivrii
Microlocal Analysis Sharp Spectral Asymptotics and Applications II Book PDF

Author : Victor Ivrii
Publisher : Springer Nature
Page : 525 pages
File Size : 44,6 Mb
Release : 2019-09-11
Category : Mathematics
ISBN : 9783030305413

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Microlocal Analysis, Sharp Spectral Asymptotics and Applications II by Victor Ivrii Pdf

The prime goal of this monograph, which comprises a total of five volumes, is to derive sharp spectral asymptotics for broad classes of partial differential operators using techniques from semiclassical microlocal analysis, in particular, propagation of singularities, and to subsequently use the variational estimates in “small” domains to consider domains with singularities of different kinds. In turn, the general theory (results and methods developed) is applied to the Magnetic Schrödinger operator, miscellaneous problems, and multiparticle quantum theory. In this volume the local spectral asymptotics of Volume I in the regular part of the domain are combined with variational estimates in the vicinity of singularities, and global asymptotics are derived in the general form. They are then applied to multiple cases and asymptotics with respect to a spectral parameter. Finally, cases in which only general methods but not the results can be applied (non-standard asymptotics) are studied.

Microlocal Analysis, Sharp Spectral Asymptotics and Applications III

Victor Ivrii
Microlocal Analysis Sharp Spectral Asymptotics and Applications III Book PDF

Author : Victor Ivrii
Publisher : Springer Nature
Page : 729 pages
File Size : 54,9 Mb
Release : 2019-09-12
Category : Mathematics
ISBN : 9783030305376

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Microlocal Analysis, Sharp Spectral Asymptotics and Applications III by Victor Ivrii Pdf

The prime goal of this monograph, which comprises a total of five volumes, is to derive sharp spectral asymptotics for broad classes of partial differential operators using techniques from semiclassical microlocal analysis, in particular, propagation of singularities, and to subsequently use the variational estimates in “small” domains to consider domains with singularities of different kinds. In turn, the general theory (results and methods developed) is applied to the Magnetic Schrödinger operator, miscellaneous problems, and multiparticle quantum theory. In this volume the methods developed in Volumes I and II are applied to the Schrödinger and Dirac operators in smooth settings in dimensions 2 and 3.