Traveling wave solutions of harmonic heat flow

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

doi:10.1007/s00526-006-0016-2

Traveling wave solutions of harmonic heat flow

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

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

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.

Original language	English (US)
Pages (from-to)	489-509
Number of pages	21
Journal	Calculus of Variations and Partial Differential Equations
Volume	26
Issue number	4
DOIs	https://doi.org/10.1007/s00526-006-0016-2
State	Published - Aug 2006

All Science Journal Classification (ASJC) codes

Analysis
Applied Mathematics

Keywords

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

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10.1007/s00526-006-0016-2

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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.",

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AU - Bertsch, M.

AU - Muratov, C. B.

AU - Primi, I.

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N2 - 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.

AB - 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.

KW - Bistable potential

KW - Calculus of variations

KW - Director field

KW - Harmonic map

KW - Singularity

KW - Traveling wave

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JO - Calculus of Variations and Partial Differential Equations

JF - Calculus of Variations and Partial Differential Equations

IS - 4

ER -

Traveling wave solutions of harmonic heat flow

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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