Shocks, Singularities and Oscillations in Nonlinear Optics and Fluid Mechanics

1. Auflage 2017
ISBN: 978-3-319-52041-4
Verlag: Springer International Publishing

Buch, Englisch, Band 17, 308 Seiten, HC runder Rücken kaschiert, Format (B × H): 160 mm x 241 mm, Gewicht: 6033 g

Reihe: Springer INdAM Series

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.

Zielgruppe

Research

Autoren/Hrsg.

Colombini, Ferruccio

Lannes, David

Del Santo, Daniele

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
• Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik
• Mathematik | Informatik Mathematik Mathematische Analysis Harmonische Analysis, Fourier-Mathematik

Inhaltsverzeichnis

1 Amplitude equations for weakly nonlinear surface waves in variational problems.- 2 Global weak solutions of PDEs for compressible media: A compactness criterion to cover new physical situations.- 3 Second microlocalization and stabilization of damped wave equations on tori.- 4 A few remarks on hyperbolic systems with Zygmund in time coefficients.- 5 Well posedness of linearized Taylor equations in magnetohydrodynamics.- 6 Strictly dissipative non uniqueness with corners.- 7 On the solvability of certain degenerate partial differential operators.- 8 Location and Weyl formula for the eigenvalues of some non self-adjoint operators.- 9 A microscopic point of view on singularities in fluid models.- 10 Geometric optics for Rayleigh pulses in nonlinear elasticity.- 11 Recent results on stability of planar detonations.

Über Autor(innen)

Ferruccio Colombini has been a Professor of Mathematical Analysis at the University of Pisa since 1986. His main interests are the theory of linear and nonlinear hyperbolic PDE's.

Daniele Del Santo is Professor of Mathematical Analysis at the University of Trieste. He works in the field of hyperbolic and parabolic operators with non-smooth coefficients.

David Lannes is CNRS Research Director at the Institut de Mathématiques de Bordeaux. He works on nonlinear PDEs and has a strong interest in applications to oceanography.