Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Absolute continuity of the solution to stochastic generalized
  Burgers-Huxley equation   The present work deals with the global solvability as well as absolute
continuity of the law of the solution to stochastic generalized Burgers-Huxley
(SGBH) equation driven by multiplicative space-time white noise in a bounded
interval of $\R$. We first prove the existence of a unique local mild solution
to SGBH equation with the help of a truncation argument and contraction mapping
principle. Then global solvability results are obtained by using uniform bounds
of the local mild solution and stopping time arguments. Later, we establish a
comparison theorem for the solution of SGBH equation having higher order
nonlinearities and it plays a crucial role in this work. Then, we discuss the
weak differentiability of the solution to SGBH equation in the Malliavin
calculus sense. Finally, we obtain the absolute continuity of the law of the
solution with respect to the Lebesgue measure on $\mathbb{R}$, and the
existence of density with the aid of comparison theorem and weak
differentiability of the solution.

27
The categories of this paper are: comp-gas
36
The categories of this paper are: cmp-lg
7
The categories of this paper are: hep-th
33
The categories of this paper are: plasm-ph
17
The categories of this paper are: q-fin
5
The categories of this paper are: gr-qc
1
The categories of this paper are: cs
24
The categories of this paper are: dg-ga
3
The categories of this paper are: physics
18
The categories of this paper are: econ
28
The categories of this paper are: alg-geom
29
The categories of this paper are: funct-an
37
The categories of this paper are: supr-con
16
The categories of this paper are: stat
32
The categories of this paper are: atom-ph
11
The categories of this paper are: hep-lat