We prove the existence of a traveling wave solution of the equation u t = Δ u + |∇u|2u in an infinitely long cylinder of radius R, which connects two locally stable and axially symmetric steady states at x 3 = ±∞. Here u is a director field with values in script S sign2 ⊂ ℝ3: |u| = 1 The traveling wave has a singular point on the cylinder axis. Letting R→ ∞ we obtain a traveling wave defined in all space.
|Original language||English (US)|
|Number of pages||21|
|Journal||Calculus of Variations and Partial Differential Equations|
|State||Published - Aug 1 2006|
All Science Journal Classification (ASJC) codes
- Applied Mathematics