Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Global existence and Hadamard differentiability of
  hysteresis-reaction-diffusion systems   We consider a class of semilinear parabolic evolution equations subject to a
hysteresis operator and a Bochner-Lebesgue integrable source term. The
underlying spatial domain is allowed to have a very general boundary. In the
first part of the paper, we apply semigroup theory to prove well-posedness and
boundedness of the solution operator. Rate independence in reaction-diffusion
systems complicates the analysis, since the reaction term acts no longer local
in time. This demands careful estimates when working with semigroup methods. In
the second part, we show Lipschitz continuity and Hadamard differentiability of
the solution operator. We use fixed point arguments to derive a representation
for the derivative in terms of the evolution system. Finally, we apply our
results to an optimal control problem in which the source term acts as a
control function and show existence of an optimal solution.

12
The categories of this paper are: nucl-th
18
The categories of this paper are: econ
27
The categories of this paper are: comp-gas
32
The categories of this paper are: atom-ph
17
The categories of this paper are: q-fin
20
The categories of this paper are: acc-phys
13
The categories of this paper are: quant-ph
25
The categories of this paper are: patt-sol
33
The categories of this paper are: plasm-ph
30
The categories of this paper are: q-alg
19
The categories of this paper are: eess
22
The categories of this paper are: chao-dyn
11
The categories of this paper are: hep-lat
21
The categories of this paper are: adap-org
1
The categories of this paper are: cs
29
The categories of this paper are: funct-an