Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On permanent and breaking waves in hyperelastic rods and rings   We prove that the only global strong solution of the periodic rod equation
vanishing in at least one point $(t_0,x_0)$ is the identically zero solution.
Such conclusion holds provided the physical parameter $\gamma$ of the model
(related to the finger deformation tensor) is outside some neighborhood of the
origin and applies in particular for the Camassa--Holm equation, corresponding
to $\gamma=1$. We also establish the analogue of this unique continuation
result in the case of non-periodic solutions defined on the whole real line
with vanishing boundary conditions at infinity. Our analysis relies on the
application of new local-in-space blowup criteria and involves the computation
of several best constants in convolution estimates and weighted Poincar\'e
inequalities.

14
The categories of this paper are: math-ph
3
The categories of this paper are: physics
37
The categories of this paper are: supr-con
9
The categories of this paper are: nlin
33
The categories of this paper are: plasm-ph
32
The categories of this paper are: atom-ph
27
The categories of this paper are: comp-gas
4
The categories of this paper are: cond-mat
36
The categories of this paper are: cmp-lg
21
The categories of this paper are: adap-org
19
The categories of this paper are: eess
11
The categories of this paper are: hep-lat
23
The categories of this paper are: solv-int
28
The categories of this paper are: alg-geom
6
The categories of this paper are: astro-ph
34
The categories of this paper are: chem-ph