Traveling wave solutions of harmonic heat flow

Authors

M. Bertsch, Istituto Per Le Applicazioni Del Calcolo Mauro Picone, Rome
C. B. Muratov, New Jersey Institute of Technology
I. Primi, Sapienza Università di Roma

Document Type

Article

Publication Date

8-1-2006

Abstract

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.

Identifier

33744517061 (Scopus)

Publication Title

Calculus of Variations and Partial Differential Equations

External Full Text Location

https://doi.org/10.1007/s00526-006-0016-2

ISSN

09442669

First Page

489

Last Page

509

Issue

4

Volume

26

Recommended Citation

Bertsch, M.; Muratov, C. B.; and Primi, I., "Traveling wave solutions of harmonic heat flow" (2006). Faculty Publications. 18871.
https://digitalcommons.njit.edu/fac_pubs/18871