We consider the heat equation for director fields, with values in the unit sphere. A variational approach is used to construct axially symmetric traveling wave solutions defined in an infinitely long cylinder. The traveling waves have a point singularity of topological degree 0 or 1. The construction of solutions with degree 0 is based on minimization of a relaxed energy.
Traveling wave solutions of the heat flow of director fields
Bertsch M;
2007
Abstract
We consider the heat equation for director fields, with values in the unit sphere. A variational approach is used to construct axially symmetric traveling wave solutions defined in an infinitely long cylinder. The traveling waves have a point singularity of topological degree 0 or 1. The construction of solutions with degree 0 is based on minimization of a relaxed energy.File in questo prodotto:
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