The logarithmic tail of Néel walls in thin films
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Submission date: 30. Aug. 2001
published in: Archive for rational mechanics and analysis, 168 (2003) 2, p. 83-113
DOI number (of the published article): 10.1007/s00205-003-0248-7
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We study the multiple scale problem of a parametrized planar 180o rotation of magnetization states in a thin ferromagnetic film known as the Néel wall transition. In this context we show that the associated Néel wall profile exhibits a very long logarithmic tail. The proof relies on limiting elliptic regularity methods on the basis of the associated Euler-Lagrange equation and symmetrization arguments on the basis of the variational principle. Finally we study the renormalized limit behaviour as the quality factor tends to zero.