Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On conditions for asymptotic stability of dissipative
  infinite-dimensional systems with intermittent damping   We study the asymptotic stability of a dissipative evolution in a Hilbert
space subject to intermittent damping. We observe that, even if the
intermittence satisfies a persistent excitation condition, if the Hilbert space
is infinite-dimensional then the system needs not being asymptotically stable
(not even in the weak sense). Exponential stability is recovered under a
generalized observability inequality, allowing for time-domains that are not
intervals. Weak asymptotic stability is obtained under a similarly generalized
unique continuation principle. Finally, strong asymptotic stability is proved
for intermittences that do not necessarily satisfy some persistent excitation
condition, evaluating their total contribution to the decay of the trajectories
of the damped system. Our results are discussed using the example of the wave
equation, Schr\"odinger's equation and, for strong stability, also the special
case of finite-dimensional systems.

33
The categories of this paper are: plasm-ph
32
The categories of this paper are: atom-ph
5
The categories of this paper are: gr-qc
0
The categories of this paper are: hep-ph
22
The categories of this paper are: chao-dyn
9
The categories of this paper are: nlin
18
The categories of this paper are: econ
24
The categories of this paper are: dg-ga
25
The categories of this paper are: patt-sol
15
The categories of this paper are: nucl-ex
35
The categories of this paper are: mtrl-th
11
The categories of this paper are: hep-lat
12
The categories of this paper are: nucl-th
31
The categories of this paper are: ao-sci
37
The categories of this paper are: supr-con
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The categories of this paper are: funct-an