Ferruccio Colombini - Böcker

This volume contains 14 research papers, which cover various topics, including blowup questions for quasilinear equations in 2-D, uniqueness results for systems of conservation laws in 1-D, conservation effects for critical nonlinear wave equations, diffraction of nonlinear waves, propagation of singularities in scattering theory,and caustics for semilinear oscillations. Other topics linked to microlocal analysis which are discussed are Sobolev spaces in Weyl-Hormander calculus, local solvability for pseudodifferential equations, and hypoellipticity for highly degenerate operators. A result for the Cauchy problem under partial analyticity assumptions and an article on the regularity of solutions for the characteristic initial boundary value problem are also included. Most of the papers contain detailed proofs which are accessible to graduate students and active researchers in connected areas.

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

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 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.