Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Model reduction of non-densely defined piecewise-smooth systems in
  Banach spaces   In this paper a model reduction technique is introduced for piecewise-smooth
(PWS) vector fields, whose trajectories fall into a Banach space, but the
domain of definition of the vector fields is a non-dense subset of the Banach
space. The vector fields depend on a parameter that can assume different
discrete values in two parts of the phase space and a continuous family of
values on the boundary that separates the two parts of the phase space. In
essence the parameter parametrizes the possible vector fields on the boundary.
The problem is to find one or more values of the parameter so that the solution
of the PWS system on the boundary satisfies certain requirements. In this paper
we require continuous solutions. Motivated by the properties of applications,
we assume that when the parameter is forced to switch between the two discrete
values, trajectories become discontinuous. Discontinuous trajectories exist in
systems whose domain of definition is non-dense. It is shown that under our
assumptions the trajectories of such PWS systems have unique forward-time
continuation when the parameter of the system switches. A finite-dimensional
reduced order model is constructed, which accounts for the discontinuous
trajectories. It is shown that this model retains uniqueness of solutions and
other properties of the original PWS system. The model reduction technique is
illustrated on a nonlinear bowed string model.

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The categories of this paper are: hep-ph
31
The categories of this paper are: ao-sci
18
The categories of this paper are: econ
12
The categories of this paper are: nucl-th
26
The categories of this paper are: bayes-an
37
The categories of this paper are: supr-con
14
The categories of this paper are: math-ph
10
The categories of this paper are: q-bio
1
The categories of this paper are: cs
30
The categories of this paper are: q-alg
23
The categories of this paper are: solv-int
34
The categories of this paper are: chem-ph
32
The categories of this paper are: atom-ph
36
The categories of this paper are: cmp-lg
7
The categories of this paper are: hep-th
22
The categories of this paper are: chao-dyn