Daniele Del Santo - Böcker

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

The present volume is a collection of papers mainly concerning Phase Space Analysis,alsoknownasMicrolocal Analysis,anditsapplicationstothetheory of Partial Di?erential Equations (PDEs). The basic idea behind this theory, at the crossing of harmonic analysis, functional analysis, quantum mechanics and algebraic analysis, is that many phenomena depend on both position and frequency (or wave numbers, or momentum) and therefore must be understood and described in the phase space. Including time and its dual variable, the energy, leads to the spa- time phase space. From this perspective major progress has been achieved in the analysis of PDEs over the last forty years, based on the development of powerful tools of microlocal analysis. A number of the following papers, all written by leading experts in their respective ?elds, are expanded versions of talks given at a meeting held in October 2007 at the Certosa di Pontignano, a former 1400 cloister sprawling on the hills surrounding Siena. The Siena workshop was in honor of Ferruccio Colombini on the occasion of his 60th birthday and it is our pleasure to dedicate to him this volume, to which a number of friends and collaborators promptly manifested their willingness to contribute. In this sense the present volume can be seen as a scienti?c portrait of Ferruccio. Many people deserve our gratitude. We would like to thank all the c- tributors as well as the people who took part in the workshop, who made a lively mathematical attendance.

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 equationsVarious levels of graduate students, along with researchers in PDEs and related fields, will find this book to be an excellent resource.ContributorsT. Alazard                                P.I. NaumkinJ.-M. Bony                              F. Nicola N. Burq                                   T. NishitaniC. Cazacu                                T. OkajiJ.-Y. Chemin                           M. PaicuE. Cordero                              A. ParmeggianiR. Danchin                               V. PetkovI. Gallagher                              M. ReissigT. Gramchev                            L. RobbianoN. Hayashi                               L. RodinoJ.Huang                                  M. Ruzhanky   D. Lannes                                J.-C. SautF. Linares                                N. ViscigliaP.B. Mucha                             P. ZhangC. Mullaert                              E. ZuazuaT. Narazaki                             C. Zuily

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 equationsVarious levels of graduate students, along with researchers in PDEs and related fields, will find this book to be an excellent resource.ContributorsT. Alazard                                P.I. NaumkinJ.-M. Bony                              F. Nicola N. Burq                                   T. NishitaniC. Cazacu                                T. OkajiJ.-Y. Chemin                           M. PaicuE. Cordero                              A. ParmeggianiR. Danchin                               V. PetkovI. Gallagher                              M. ReissigT. Gramchev                            L. RobbianoN. Hayashi                               L. RodinoJ.Huang                                  M. Ruzhanky   D. Lannes                                J.-C. SautF. Linares                                N. ViscigliaP.B. Mucha                             P. ZhangC. Mullaert                              E. ZuazuaT. Narazaki                             C. Zuily

The contributions contained in the volume, written by leading experts in their respective fields, are expanded versions of talks given at the INDAM Workshop "Anomalies in Partial Differential Equations" held in September 2019 at the Istituto Nazionale di Alta Matematica, Dipartimento di Matematica "Guido Castelnuovo", Università di Roma "La Sapienza". The volume contains results for well-posedness and local solvability  for linear models with low regular coefficients. Moreover, nonlinear dispersive models (damped waves, p-evolution models) are discussed from the point of view of  critical exponents, blow-up phenomena or decay estimates for Sobolev solutions. Some contributions are devoted to models from applications as traffic flows, Einstein-Euler systems or stochastic PDEs as well. Finally, several contributions from Harmonic and Time-Frequency Analysis, in which the authors are interested in  the action of localizing operators or the description of wave front sets, complete the volume.

The contributions contained in the volume, written by leading experts in their respective fields, are expanded versions of talks given at the INDAM Workshop "Anomalies in Partial Differential Equations" held in September 2019 at the Istituto Nazionale di Alta Matematica, Dipartimento di Matematica "Guido Castelnuovo", Università di Roma "La Sapienza". The volume contains results for well-posedness and local solvability  for linear models with low regular coefficients. Moreover, nonlinear dispersive models (damped waves, p-evolution models) are discussed from the point of view of  critical exponents, blow-up phenomena or decay estimates for Sobolev solutions. Some contributions are devoted to models from applications as traffic flows, Einstein-Euler systems or stochastic PDEs as well. Finally, several contributions from Harmonic and Time-Frequency Analysis, in which the authors are interested in  the action of localizing operators or the description of wave front sets, complete the volume.

The book collects the most relevant results from the INdAM Workshop "Shocks, Singularities and Oscillations in Nonlinear Optics and Fluid Mechanics" held in Rome, September 14-18, 2015. The contributions discuss recent major advances in the study of nonlinear hyperbolic systems, addressing general theoretical issues such as symmetrizability, singularities, low regularity or dispersive perturbations. It also investigates several physical phenomena where such systems are relevant, such as nonlinear optics, shock theory (stability, relaxation) and fluid mechanics (boundary layers, water waves, Euler equations, geophysical flows, etc.). It is a valuable resource for researchers in these fields.