Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Stochastic Burgers-Huxley Equations: Global Solvability, Large
  Deviations and Ergodicity   In this work, we consider the stochastic Burgers-Huxley equation perturbed by
multiplicative Gaussian noise, and discuss about the global solvability results
and asymptotic behavior of solutions. We show the existence of a global strong
solution of the stochastic Burgers-Huxley equation, by making use of a local
monotonicity property of the linear and nonlinear operators and a stochastic
generalization of localized version of the Minty-Browder technique. We then
discuss about the inviscid limit of the stochastic Burgers-Huxley equation to
Burgers as well as Huxley equations. By considering the noise to be additive
Gaussian, Exponential estimates for exit from a ball of radius $R$ by time $T$
for solutions of the stochastic Burgers-Huxley equation is derived, and then
studied in the context of Freidlin-Wentzell type large deviations principle.
Finally, we establish the existence of a unique ergodic and strongly mixing
invariant measure for the stochastic Burgers-Huxley equation with additive
Gaussian noise, using the exponential stability of solutions.

23
The categories of this paper are: solv-int
18
The categories of this paper are: econ
16
The categories of this paper are: stat
12
The categories of this paper are: nucl-th
29
The categories of this paper are: funct-an
19
The categories of this paper are: eess
32
The categories of this paper are: atom-ph
0
The categories of this paper are: hep-ph
3
The categories of this paper are: physics
9
The categories of this paper are: nlin
7
The categories of this paper are: hep-th
36
The categories of this paper are: cmp-lg
27
The categories of this paper are: comp-gas
25
The categories of this paper are: patt-sol
4
The categories of this paper are: cond-mat
5
The categories of this paper are: gr-qc