Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On well-posedness, stability, and bifurcation for the axisymmetric
  surface diffusion flow   In this article, we study the axisymmetric surface diffusion flow (ASD), a
fourth-order geometric evolution law. In particular, we prove that ASD
generates a real analytic semiflow in the space of (2 + \alpha)-little-H\"older
regular surfaces of revolution embedded in R^3 and satisfying periodic boundary
conditions. We also give conditions for global existence of solutions and prove
that solutions are real analytic in time and space. Further, we investigate the
geometric properties of solutions to ASD. Utilizing a connection to
axisymmetric surfaces with constant mean curvature, we characterize the
equilibria of ASD. Then, focusing on the family of cylinders, we establish
results regarding stability, instability and bifurcation behavior, with the
radius acting as a bifurcation parameter for the problem.

20
The categories of this paper are: acc-phys
28
The categories of this paper are: alg-geom
37
The categories of this paper are: supr-con
1
The categories of this paper are: cs
19
The categories of this paper are: eess
3
The categories of this paper are: physics
36
The categories of this paper are: cmp-lg
0
The categories of this paper are: hep-ph
8
The categories of this paper are: hep-ex
6
The categories of this paper are: astro-ph
25
The categories of this paper are: patt-sol
33
The categories of this paper are: plasm-ph
5
The categories of this paper are: gr-qc
11
The categories of this paper are: hep-lat
29
The categories of this paper are: funct-an
34
The categories of this paper are: chem-ph