Regularization of moving boundaries in a Laplacian field by a mixed dirichlet-neumann boundary condition: Exact results

B. Meulenbroek, U. Ebert, L. Schäfer

Research output: Contribution to journalArticleAcademicpeer-review

23 Citations (Scopus)
72 Downloads (Pure)

Abstract

The dynamics of ionization fronts that generate a conducting body are in the simplest approximation equivalent to viscous fingering without regularization. Going beyond this approximation, we suggest that ionization fronts can be modeled by a mixed Dirichlet-Neumann boundary condition. We derive exact uniformly propagating solutions of this problem in 2D and construct a single partial differential equation governing small perturbations of these solutions. For some parameter value, this equation can be solved analytically, which shows rigorously that the uniformly propagating solution is linearly convectively stable and that the asymptotic relaxation is universal and exponential in time.
Original languageEnglish
Article number195004
Pages (from-to)195004-1/4
Number of pages4
JournalPhysical Review Letters
Volume95
Issue number19
DOIs
Publication statusPublished - 2005

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