Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Optimal Control for a Nonlinear Stochastic Parabolic Model of Language
  Competition   In this investigation, an optimal control problem for a stochastic
mathematical model of language competition is studied. We have considered the
stochastic model of language competition by adding the stochastic terms to the
deterministic model to take into account the random perturbations and
uncertainties caused by the environment to have more reliable model. The model
has formulated the population densities of the speakers of two languages, which
are competing against each other to be saved from destruction, attract more
speakers and so on, using two nonlinear stochastic parabolic equations. Four
factors including the status of the languages and the growth rates of the
populations are considered as the control variables (which can be controlled by
the speakers of the populations or policy makers who make decisions for the
populations for particular purposes) to control the evolution of the population
densities. Then, the optimal control problem for the stochastic model of
language competition is studied. Employing the tangent-normal cone techniques,
the Ekeland variational principle and other theorems proved throughout the
paper, we have shown there exists unique stochastic optimal control. We have
also presented the exact form of the optimal control in terms of stochastic
adjoint states.

33
The categories of this paper are: plasm-ph
36
The categories of this paper are: cmp-lg
14
The categories of this paper are: math-ph
20
The categories of this paper are: acc-phys
4
The categories of this paper are: cond-mat
18
The categories of this paper are: econ
6
The categories of this paper are: astro-ph
9
The categories of this paper are: nlin
19
The categories of this paper are: eess
29
The categories of this paper are: funct-an
15
The categories of this paper are: nucl-ex
16
The categories of this paper are: stat
37
The categories of this paper are: supr-con
35
The categories of this paper are: mtrl-th
7
The categories of this paper are: hep-th
12
The categories of this paper are: nucl-th