Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Existence and nonexistence theorems for global weak solutions to
  quasilinear wave equations for the elasticity   In this paper, by using the theory of compensated compactness coupled with
the kinetic formulation by Lions, Perthame, Souganidis and Tadmor
\cite{LPT,LPS}, we prove the existence and nonexistence of global generalized
(nonnegative) solutions of the nonlinearly degenerate wave equations $v_{tt} =c
(|v|^{s-1} v)_{xx}$ with the nonnegative initial data $v_{0}(x)$ and $ s > 1$.
This result is an extension of the results in the second author's paper
\cite{Su}, where the existence and the nonexistence of the unique global
classical solution were studied with a threshold on $\int_{-\infty}^{\infty}
v_{1}(x) dx$ and the non-degeneracy condition $ v_{0}(x) \geq c_{0} > 0$ on the
initial data.

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The categories of this paper are: q-bio
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The categories of this paper are: dg-ga
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The categories of this paper are: eess
34
The categories of this paper are: chem-ph
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The categories of this paper are: atom-ph
18
The categories of this paper are: econ
31
The categories of this paper are: ao-sci
28
The categories of this paper are: alg-geom
14
The categories of this paper are: math-ph
21
The categories of this paper are: adap-org
29
The categories of this paper are: funct-an
0
The categories of this paper are: hep-ph
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The categories of this paper are: nlin
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The categories of this paper are: q-fin
37
The categories of this paper are: supr-con
6
The categories of this paper are: astro-ph