Phase Space Analysis of Partial Differential Equations - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Phase Space Analysis of Partial Differential Equations write by Antonio Bove. This book was released on 2007-12-28. Phase Space Analysis of Partial Differential Equations available in PDF, EPUB and Kindle. 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
Methods for Partial Differential Equations
Methods for Partial Differential Equations - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Methods for Partial Differential Equations write by Marcelo R. Ebert. This book was released on 2018-02-23. Methods for Partial Differential Equations available in PDF, EPUB and Kindle. 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.
Advances in Phase Space Analysis of Partial Differential Equations
Advances in Phase Space Analysis of Partial Differential Equations - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Advances in Phase Space Analysis of Partial Differential Equations write by Antonio Bove. This book was released on 2009-09-18. Advances in Phase Space Analysis of Partial Differential Equations available in PDF, EPUB and Kindle. 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.
Harmonic Analysis in Phase Space. (AM-122), Volume 122
Harmonic Analysis in Phase Space. (AM-122), Volume 122 - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Harmonic Analysis in Phase Space. (AM-122), Volume 122 write by Gerald B. Folland. This book was released on 2016-03-02. Harmonic Analysis in Phase Space. (AM-122), Volume 122 available in PDF, EPUB and Kindle. 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.
Metrics on the Phase Space and Non-Selfadjoint Pseudo-Differential Operators
Metrics on the Phase Space and Non-Selfadjoint Pseudo-Differential Operators - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Metrics on the Phase Space and Non-Selfadjoint Pseudo-Differential Operators write by Nicolas Lerner. This book was released on 2011-01-30. Metrics on the Phase Space and Non-Selfadjoint Pseudo-Differential Operators available in PDF, EPUB and Kindle. 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.
