Back to Search
Start Over
Cross-shaped and degenerate singularities in an unstable elliptic free boundary problem
- Source :
-
Journal of Differential Equations . Sep2006, Vol. 228 Issue 2, p633-640. 8p. - Publication Year :
- 2006
-
Abstract
- Abstract: We investigate singular and degenerate behavior of solutions of the unstable free boundary problem First, we construct a solution that is not of class and whose free boundary consists of four arcs meeting in a cross-shaped singularity. This solution is completely unstable/repulsive from above and below which would make it hard to get by the usual methods, and even numerics is nontrivial. We also show existence of a degenerate solution. This answers two of the open questions in the paper [R. Monneau, G.S. Weiss, An unstable elliptic free boundary problem arising in solid combustion, http://arxiv.org/abs/math.AP/0507315, submitted for publication]. [Copyright &y& Elsevier]
Details
- Language :
- English
- ISSN :
- 00220396
- Volume :
- 228
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- Journal of Differential Equations
- Publication Type :
- Academic Journal
- Accession number :
- 21913271
- Full Text :
- https://doi.org/10.1016/j.jde.2005.11.008