Dielectric breakdown model at small eta: pole dynamics.
We consider the dielectric breakdown model in the limit eta-->0(+). This is shown to lead to Sivashinsky's equation. We show that a particular configuration of poles is linearly stable, in analogy to the stability of the 1/2 finger for diffusion limited aggregation, and compute exactly the eigenvalues of the stability matrix.
Center for Nonlinear Studies and Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545, USA. hastings@cnls.lanl.gov
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Hastings