Traveling wave solutions of harmonic heat flow

M. Bertsch, C. B. Muratov, I. Primi

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


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 languageEnglish (US)
Pages (from-to)489-509
Number of pages21
JournalCalculus of Variations and Partial Differential Equations
Issue number4
StatePublished - Aug 2006

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics


  • Bistable potential
  • Calculus of variations
  • Director field
  • Harmonic map
  • Singularity
  • Traveling wave


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