Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the obstacle problem for the 1D wave equation   Our goal is to review the known theory on the one-dimensional obstacle
problem for the wave equation, and to discuss some extensions. We introduce the
setting established by Schatzman within which existence and uniqueness of
solutions can be proved, and we prove that (in some suitable systems of
coordinates) the Lipschitz norm is preserved after collision. As a consequence,
we deduce that solutions to the obstacle problem (both simple and double) for
the wave equation have bounded Lipschitz norm at all times. Finally, we discuss
the validity of an explicit formula for the solution that was found by
Bamberger and Schatzman.

13
The categories of this paper are: quant-ph
4
The categories of this paper are: cond-mat
18
The categories of this paper are: econ
36
The categories of this paper are: cmp-lg
25
The categories of this paper are: patt-sol
21
The categories of this paper are: adap-org
9
The categories of this paper are: nlin
0
The categories of this paper are: hep-ph
16
The categories of this paper are: stat
28
The categories of this paper are: alg-geom
7
The categories of this paper are: hep-th
26
The categories of this paper are: bayes-an
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The categories of this paper are: gr-qc
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The categories of this paper are: nucl-ex
3
The categories of this paper are: physics
14
The categories of this paper are: math-ph