Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8898168 | Annales de l'Institut Henri Poincare (C) Non Linear Analysis | 2017 | 11 Pages |
Abstract
Our results show that the issue strongly depends on the initial data and reveal a rather rich variety of phenomena. For any smooth bounded domain, we construct initial data such that the loss of boundary conditions occurs everywhere on the boundary, as well as initial data for which no loss of boundary conditions occurs in spite of gradient blowup. Actually, we show that the latter possibility is rather exceptional. More generally, we show that the set of the points where boundary conditions are lost, can be prescribed to be arbitrarily close to any given open subset of the boundary.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Alessio Porretta, Philippe Souplet,