Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A boundary control problem for a possibly singular phase field system
  with dynamic boundary conditions   This paper deals with an optimal control problem related to a phase field
system of Caginalp type with a dynamic boundary condition for the temperature.
The control placed in the dynamic boundary condition acts on a part of the
boundary. The analysis carried out in this paper proves the existence of an
optimal control for a general class of potentials, possibly singular. The study
includes potentials for which the derivatives may not exist, these being
replaced by well-defined subdifferentials. Under some stronger assumptions on
the structure parameters and on the potentials (namely for the regular and the
logarithmic case having single-valued derivatives), the first order necessary
optimality conditions are derived and expressed in terms of the boundary trace
of the first adjoint variable.

17
The categories of this paper are: q-fin
19
The categories of this paper are: eess
14
The categories of this paper are: math-ph
25
The categories of this paper are: patt-sol
35
The categories of this paper are: mtrl-th
15
The categories of this paper are: nucl-ex
6
The categories of this paper are: astro-ph
16
The categories of this paper are: stat
26
The categories of this paper are: bayes-an
7
The categories of this paper are: hep-th
10
The categories of this paper are: q-bio
23
The categories of this paper are: solv-int
0
The categories of this paper are: hep-ph
20
The categories of this paper are: acc-phys
34
The categories of this paper are: chem-ph
28
The categories of this paper are: alg-geom