Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Energy-dissipation balance of a smooth moving crack   In this paper we provide necessary and sufficient conditions in order to
guarantee the energy-dissipation balance of a Mode III crack, growing on a
prescribed smooth path. Moreover, we characterize the singularity of the
displacement near the crack tip, generalizing the result in [S.Nicaise,
A.M.Sandig - \textit{J. Math. Anal. Appl.} 2007] valid for straight fractures.

7
The categories of this paper are: hep-th
0
The categories of this paper are: hep-ph
18
The categories of this paper are: econ
32
The categories of this paper are: atom-ph
19
The categories of this paper are: eess
30
The categories of this paper are: q-alg
22
The categories of this paper are: chao-dyn
8
The categories of this paper are: hep-ex
10
The categories of this paper are: q-bio
31
The categories of this paper are: ao-sci
23
The categories of this paper are: solv-int
26
The categories of this paper are: bayes-an
25
The categories of this paper are: patt-sol
11
The categories of this paper are: hep-lat
5
The categories of this paper are: gr-qc
29
The categories of this paper are: funct-an