Abstract
In this paper, we study the short time behavior of the solutions of a sequence of Ginzburg-Landau equations indexed by ε. We prove that under appropriate assumptions on the initial data, solutions converge to ±1 in short time and behave like the one-dimensional traveling wave across the interface. In particular, energy remains uniformly bounded in ε.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 477-491 |
| Number of pages | 15 |
| Journal | Journal of Geometric Analysis |
| Volume | 7 |
| Issue number | 3 |
| DOIs | |
| State | Published - 1997 |
| Externally published | Yes |
All Science Journal Classification (ASJC) codes
- Geometry and Topology
Keywords
- Ginzburg-Landau equation
- Maximum principle
- Traveling waves