Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Non-autonomous stochastic evolution equations and applications to
  stochastic partial differential equations   In this paper we study the following non-autonomous stochastic evolution
equation on a UMD Banach space $E$ with type 2,
  {equation}\label{eq:SEab}\tag{SE} {{aligned} dU(t) & = (A(t)U(t) + F(t,U(t)))
dt + B(t,U(t)) dW_H(t), \quad t\in [0,T],
  U(0) & = u_0. {aligned}. {equation}
  Here $(A(t))_{t\in [0,T]}$ are unbounded operators with domains
$(D(A(t)))_{t\in [0,T]}$ which may be time dependent. We assume that
$(A(t))_{t\in [0,T]}$ satisfies the conditions of Acquistapace and Terreni. The
functions $F$ and $B$ are nonlinear functions defined on certain interpolation
spaces and $u_0\in E$ is the initial value. $W_H$ is a cylindrical Brownian
motion on a separable Hilbert space $H$.
  Under Lipschitz and linear growth conditions we show that there exists a
unique mild solution of \eqref{eq:SEab}. Under assumptions on the interpolation
spaces we extend the factorization method of Da Prato, Kwapie\'n, and Zabczyk,
to obtain space-time regularity results for the solution $U$ of
\eqref{eq:SEab}. For Hilbert spaces $E$ we obtain a maximal regularity result.
The results improve several previous results from the literature.
  The theory is applied to a second order stochastic partial differential
equation which has been studied by Sanz-Sol\'e and Vuillermot. This leads to
several improvements of their result.

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The categories of this paper are: chem-ph
11
The categories of this paper are: hep-lat
31
The categories of this paper are: ao-sci
17
The categories of this paper are: q-fin
19
The categories of this paper are: eess
20
The categories of this paper are: acc-phys
21
The categories of this paper are: adap-org
30
The categories of this paper are: q-alg
35
The categories of this paper are: mtrl-th
25
The categories of this paper are: patt-sol
13
The categories of this paper are: quant-ph
16
The categories of this paper are: stat
14
The categories of this paper are: math-ph
4
The categories of this paper are: cond-mat
5
The categories of this paper are: gr-qc
27
The categories of this paper are: comp-gas