Global Dynamics, Blow-Up, and Bianchi Cosmology
Abstract
Many central problems in geometry, topology, and mathematical physics lead to questions concerning the long-time dynamics of solutions to ordinary and partial differential equations. Examples range from the Einstein field equations of general relativity to quasilinear reaction-advection-diffusion equations of parabolic type. Specific questions concern the convergence to equilibria, the existence of periodic, homoclinic, and heteroclinic solutions, and the existence and geometric structure of global attractors. On the other hand, many solutions develop singularities in finite time. The singularities have to be analyzed in detail before attempting to extend solutions beyond their singularities, or to understand their geometry in conjunction with globally bounded solutions. In this context we have also aimed at global qualitative descriptions of blow-up and grow-up phenomena.
Cite
@article{arxiv.1607.04600,
title = {Global Dynamics, Blow-Up, and Bianchi Cosmology},
author = {Nitsan Ben-Gal and Bernhard Brehm and Johannes Buchner and Juliette Hell and Anna Karnauhova and Stefan Liebscher and Alan Rendall and Brian Smith and Hannes Stuke and Martin Väth and Bernold Fiedler},
journal= {arXiv preprint arXiv:1607.04600},
year = {2016}
}
Comments
39 pages, 16 figures, survey