Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Singular asymptotic expansion of the exact control for a linear model of
  the Rayleigh beam   The Petrowsky type equation $y_{tt}^\eps+\eps y_{xxxx}^\eps - y_{xx}^\eps=0$,
$\eps>0$ encountered in linear beams theory is null controllable through
Neumann boundary controls. Due to the boundary layer of size of order
$\sqrt{\eps}$ occurring at the extremities, these boundary controls get
singular as $\eps$ goes to $0$. Using the matched asymptotic method, we
describe the boundary layer of the solution $y^\eps$ then derive a rigorous
second order asymptotic expansion of the control of minimal $L^2-$norm, with
respect to the parameter $\eps$. In particular, we recover that the leading
term of the expansion is a null Dirichlet control for the limit hyperbolic wave
equation, in agreement with earlier results due to J-.L. Lions in the eighties.
Numerical experiments support the analysis.

3
The categories of this paper are: physics
21
The categories of this paper are: adap-org
13
The categories of this paper are: quant-ph
10
The categories of this paper are: q-bio
22
The categories of this paper are: chao-dyn
15
The categories of this paper are: nucl-ex
24
The categories of this paper are: dg-ga
31
The categories of this paper are: ao-sci
26
The categories of this paper are: bayes-an
11
The categories of this paper are: hep-lat
35
The categories of this paper are: mtrl-th
34
The categories of this paper are: chem-ph
30
The categories of this paper are: q-alg
8
The categories of this paper are: hep-ex
4
The categories of this paper are: cond-mat
5
The categories of this paper are: gr-qc