Regularization of moving boundaries in a Laplacian field by a mixed Dirichlet-Neumann boundary condition: exact results

Details Regularization of moving boundaries in a Laplacian field by a mixed Dirichlet-Neumann boundary condition: exact results Regularization of moving boundaries in a Laplacian field by a mixed Dirichlet-Neumann boundary condition: exact results

2005-07-11

arxiv.org/abs/nlin/0507019v1

Phys. Rev. Lett. 95, 195004 (2005)

Nonlinear Sciences

Pattern Formation and Solitons

4 pages, 1 figure

Scientific paper

10.1103/PhysRevLett.95.195004

The dynamics of ionization fronts that generate a conducting body, are in 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 that the uniformly propagating solution is linearly convectively stable.

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