We prove the existence of a traveling wave solution of the equation u(t) = Delta u + vertical bar del u vertical bar(2)u in an infinitely long cylinder of radius R, which connects two locally stable and axially symmetric steady states at x(3) = +/-infinity. Here a is a director field with values in S-2 subset of R-3: vertical bar u vertical bar = 1. The traveling wave has a singular point on the cylinder axis. Letting R -> infinity we obtain a traveling wave defined in all space.
Traveling wave solutions of harmonic heat flow
Muratov, CB;
2006-01-01
Abstract
We prove the existence of a traveling wave solution of the equation u(t) = Delta u + vertical bar del u vertical bar(2)u in an infinitely long cylinder of radius R, which connects two locally stable and axially symmetric steady states at x(3) = +/-infinity. Here a is a director field with values in S-2 subset of R-3: vertical bar u vertical bar = 1. The traveling wave has a singular point on the cylinder axis. Letting R -> infinity we obtain a traveling wave defined in all space.File in questo prodotto:
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