Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Optimal treatment for a phase field system of Cahn-Hilliard type
  modeling tumor growth by asymptotic scheme   We consider a particular phase field system which physical context is that of
tumor growth dynamics. The model we deal with consists of a Cahn-Hilliard type
equation governing the evolution of the phase variable which takes into account
the tumor cells proliferation in the tissue coupled with a reaction-diffusion
equation for the nutrient. This model has already been investigated from the
viewpoint of well-posedness, long time behavior, and asymptotic analyses as
some parameters go to zero. Starting from these results, we aim to face a
related optimal control problem by employing suitable asymptotic schemes. In
this direction, further assumptions have to be required. Mainly, we ought to
impose some quite general growth conditions for the involved potential and a
smallness restriction for a parameter appearing in the system we are going to
face. We provide existence of optimal controls and a necessary condition that
an optimal control has to satisfy has been characterized as well.

19
The categories of this paper are: eess
31
The categories of this paper are: ao-sci
1
The categories of this paper are: cs
25
The categories of this paper are: patt-sol
7
The categories of this paper are: hep-th
13
The categories of this paper are: quant-ph
4
The categories of this paper are: cond-mat
35
The categories of this paper are: mtrl-th
33
The categories of this paper are: plasm-ph
12
The categories of this paper are: nucl-th
3
The categories of this paper are: physics
17
The categories of this paper are: q-fin
8
The categories of this paper are: hep-ex
10
The categories of this paper are: q-bio
5
The categories of this paper are: gr-qc
27
The categories of this paper are: comp-gas