Control of blow-up singularities for nonlinear wave equations
Analysis of PDEs
2017-09-25 v1 Pattern Formation and Solitons
Abstract
While the global boundary control of nonlinear wave equations that exhibit blow-up is generally impossible, we show on a typical example, motivated by laser breakdown, that it is possible to control solutions with small data so that they blow up on a prescribed compact set bounded away from the boundary of the domain. This is achieved using the representation of singular solutions with prescribed blow-up surface given by Fuchsian reduction. We outline on this example simple methods that may be of wider applicability.
Cite
@article{arxiv.1709.07746,
title = {Control of blow-up singularities for nonlinear wave equations},
author = {Satyanad Kichenassamy},
journal= {arXiv preprint arXiv:1709.07746},
year = {2017}
}