We prove the existence of a traveling wave solution u of the harmonic heat flow in an infinitely long cylinder of radius R, which connects two locally stable and axially symmetric steady states at + and - infinity infinity. Here u is a director field, with values in the unit sphere. The traveling wave has a singular point on the cylinder axis. As R goes to infinity we obtain a traveling wave defined in all space.
Traveling wave solutions of harmonic heat flow
Bertsch M;
2006
Abstract
We prove the existence of a traveling wave solution u of the harmonic heat flow in an infinitely long cylinder of radius R, which connects two locally stable and axially symmetric steady states at + and - infinity infinity. Here u is a director field, with values in the unit sphere. The traveling wave has a singular point on the cylinder axis. As R goes to infinity we obtain a traveling wave defined in all space.File in questo prodotto:
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