Nonlinear PDEs, Their Geometry, and Applications

Proceedings of the Wis¿a 18 Summer School
1. Auflage 2019
ISBN: 978-3-030-17030-1
Verlag: Springer International Publishing

Buch, Englisch, 279 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 458 g

Reihe: Tutorials, Schools, and Workshops in the Mathematical Sciences

This volume presents lectures given at the Summer School Wisla 18: Nonlinear PDEs, Their Geometry, and Applications, which took place from August 20 - 30th, 2018 in Wisla, Poland, and was organized by the Baltic Institute of Mathematics. The lectures in the first part of this volume were delivered by experts in nonlinear differential equations and their applications to physics. Original research articles from members of the school comprise the second part of this volume. Much of the latter half of the volume complements the methods expounded in the first half by illustrating additional applications of geometric theory of differential equations. Various subjects are covered, providing readers a glimpse of current research. Other topics covered include thermodynamics, meteorology, and the Monge–Ampère equations.
Researchers interested in the applications of nonlinear differential equations to physics will find this volume particularly useful. A knowledge ofdifferential geometry is recommended for the first portion of the book, as well as a familiarity with basic concepts in physics.

Zielgruppe

Graduate

Autoren/Hrsg.

Kycia, Rados¿aw A.

Kycia, Radoslaw A.

Schneider, Eivind

Ulan, Maria

Fachgebiete

• Mathematik | Informatik Mathematik Geometrie Differentialgeometrie
• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen

Inhaltsverzeichnis

Part I Lectures.- Contact Geometry, Measurement and Thermodynamics.- Lectures on Geometry of Monge-Ampere Equations with Maple.- Geometry of Monge-Ampere structures.- Introduction to symbolic computations in differential geometry.- Part II Participants' Contributions.- On the geometry arising in some meteorological models in two and three dimensions.- Gas flow with phase transitions: thermodynamics and the Navier-Stokes equations.- Differential invariants in thermodynamics.- Monge-Ampere grassmannians, characteristic classes and all that.- Weak inverse problem of calculus of variations for geodesic mappings and relation to harmonic maps.- Integrability of geodesics of totally geodesic metrics.