Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Uniqueness and existence of spirals moving by forced mean curvature
  motion   In this paper, we study the motion of spirals by mean curvature type motion
in the (two dimensional) plane. Our motivation comes from dislocation dynamics;
in this context, spirals appear when a screw dislocation line reaches the
surface of a crystal. The first main result of this paper is a comparison
principle for the corresponding parabolic quasi-linear equation. As far as
motion of spirals are concerned, the novelty and originality of our setting and
results come from the fact that, first, the singularity generated by the
attached end point of spirals is taken into account for the first time, and
second, spirals are studied in the whole space. Our second main result states
that the Cauchy problem is well-posed in the class of sub-linear weak
(viscosity) solutions. We also explain how to get the existence of smooth
solutions when initial data satisfy an additional compatibility condition.

1
The categories of this paper are: cs
4
The categories of this paper are: cond-mat
33
The categories of this paper are: plasm-ph
10
The categories of this paper are: q-bio
35
The categories of this paper are: mtrl-th
31
The categories of this paper are: ao-sci
17
The categories of this paper are: q-fin
20
The categories of this paper are: acc-phys
27
The categories of this paper are: comp-gas
0
The categories of this paper are: hep-ph
36
The categories of this paper are: cmp-lg
15
The categories of this paper are: nucl-ex
16
The categories of this paper are: stat
19
The categories of this paper are: eess
25
The categories of this paper are: patt-sol
32
The categories of this paper are: atom-ph