Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Long time behavior of dynamic solution to Peierls--Nabarro dislocation
  model   In this paper we study the relaxation process of Peierls-Nabarro dislocation
model, which is a gradient flow with singular nonlocal energy and double well
potential describing how the materials relax to its equilibrium with the
presence of a dislocation. We prove the dynamic solution to Peierls-Nabarro
model will converge exponentially to a shifted steady profile which is uniquely
determined.

20
The categories of this paper are: acc-phys
4
The categories of this paper are: cond-mat
3
The categories of this paper are: physics
35
The categories of this paper are: mtrl-th
26
The categories of this paper are: bayes-an
16
The categories of this paper are: stat
7
The categories of this paper are: hep-th
13
The categories of this paper are: quant-ph
30
The categories of this paper are: q-alg
24
The categories of this paper are: dg-ga
8
The categories of this paper are: hep-ex
14
The categories of this paper are: math-ph
34
The categories of this paper are: chem-ph
5
The categories of this paper are: gr-qc
31
The categories of this paper are: ao-sci
28
The categories of this paper are: alg-geom