Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A moving boundary model motivated by electric breakdown: II. Initial
  value problem   An interfacial approximation of the streamer stage in the evolution of sparks
and lightning can be formulated as a Laplacian growth model regularized by a
'kinetic undercooling' boundary condition. Using this model we study both the
linearized and the full nonlinear evolution of small perturbations of a
uniformly translating circle. Within the linear approximation analytical and
numerical results show that perturbations are advected to the back of the
circle, where they decay. An initially analytic interface stays analytic for
all finite times, but singularities from outside the physical region approach
the interface for $t\to\infty$, which results in some anomalous relaxation at
the back of the circle. For the nonlinear evolution numerical results indicate
that the circle is the asymptotic attractor for small perturbations, but larger
perturbations may lead to branching. We also present results for more general
initial shapes, which demonstrate that regularization by kinetic undercooling
cannot guarantee smooth interfaces globally in time.

29
The categories of this paper are: funct-an
8
The categories of this paper are: hep-ex
12
The categories of this paper are: nucl-th
30
The categories of this paper are: q-alg
16
The categories of this paper are: stat
15
The categories of this paper are: nucl-ex
22
The categories of this paper are: chao-dyn
35
The categories of this paper are: mtrl-th
6
The categories of this paper are: astro-ph
27
The categories of this paper are: comp-gas
28
The categories of this paper are: alg-geom
5
The categories of this paper are: gr-qc
34
The categories of this paper are: chem-ph
19
The categories of this paper are: eess
4
The categories of this paper are: cond-mat
37
The categories of this paper are: supr-con