Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Equivalent formulations of the oxygen depletion problem, other implicit
  free boundary value problems, and implications for numerical approximation   The Oxygen Depletion problem is an implicit free boundary value problem. The
dynamics allow topological changes in the free boundary. We show several
mathematical formulations of this model from the literature and give a new
formulation based on a gradient flow with constraint. All formulations are
shown to be equivalent. We explore the possibilities for the numerical
approximation of the problem that arise from the different formulations. We
show a convergence result for an approximation based on the gradient flow with
constraint formulation that applies to the general dynamics including
topological changes. More general (vector, higher order) implicit free boundary
value problems are discussed. Several open problems are described.

8
The categories of this paper are: hep-ex
4
The categories of this paper are: cond-mat
27
The categories of this paper are: comp-gas
37
The categories of this paper are: supr-con
13
The categories of this paper are: quant-ph
19
The categories of this paper are: eess
18
The categories of this paper are: econ
23
The categories of this paper are: solv-int
29
The categories of this paper are: funct-an
0
The categories of this paper are: hep-ph
10
The categories of this paper are: q-bio
20
The categories of this paper are: acc-phys
17
The categories of this paper are: q-fin
21
The categories of this paper are: adap-org
12
The categories of this paper are: nucl-th
35
The categories of this paper are: mtrl-th