Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A two-stage numerical approach for the sparse initial source
  identification of a diffusion-advection equation   We consider the problem of identifying a sparse initial source condition to
achieve a given state distribution of a diffusion-advection partial
differential equation after a given final time. The initial condition is
assumed to be a finite combination of Dirac measures. The locations and
intensities of this initial condition are required to be identified. This
problem is known to be exponentially ill-posed because of the strong diffusive
and smoothing effects. We propose a two-stage numerical approach to treat this
problem. At the first stage, to obtain a sparse initial condition with the
desire of achieving the given state subject to a certain tolerance, we propose
an optimal control problem involving sparsity-promoting and
ill-posedness-avoiding terms in the cost functional, and introduce a
generalized primal-dual algorithm for this optimal control problem. At the
second stage, the initial condition obtained from the optimal control problem
is further enhanced by identifying its locations and intensities in its
representation of the combination of Dirac measures. This two-stage numerical
approach is shown to be easily implementable and its efficiency in short time
horizons is promisingly validated by the results of numerical experiments. Some
discussions on long time horizons are also included.

25
The categories of this paper are: patt-sol
11
The categories of this paper are: hep-lat
21
The categories of this paper are: adap-org
30
The categories of this paper are: q-alg
3
The categories of this paper are: physics
26
The categories of this paper are: bayes-an
18
The categories of this paper are: econ
24
The categories of this paper are: dg-ga
12
The categories of this paper are: nucl-th
32
The categories of this paper are: atom-ph
31
The categories of this paper are: ao-sci
19
The categories of this paper are: eess
37
The categories of this paper are: supr-con
8
The categories of this paper are: hep-ex
0
The categories of this paper are: hep-ph
9
The categories of this paper are: nlin