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.
All Science Journal Classification (ASJC) codes
- Geometry and Topology
- Ginzburg-Landau equation
- Maximum principle
- Traveling waves