Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Stochastic generalized porous media equations driven by L\'{e}vy noise
  with increasing Lipschitz nonlinearities   We establish the existence and uniqueness of strong solutions to stochastic
porous media equations driven by L\'{e}vy noise on a $\sigma$-finite measure
space $(E,\mathcal{B}(E),\mu)$, and with the Laplacian replaced by a negative
definite self-adjoint operator. The coefficient $\Psi$ is only assumed to
satisfy the increasing Lipschitz nonlinearity assumption, without the
restriction $r\Psi(r)\rightarrow\infty$ as $r\rightarrow\infty$ for
$L^2(\mu)$-initial data. We also extend the state space, which avoids the
transience assumption on $L$ or the boundedness of $L^{-1}$ in
$L^{r+1}(E,\mathcal{B}(E),\mu)$ for some $r\geq1$. Examples of the negative
definite self-adjoint operators include fractional powers of the Laplacian,
i.e. $L=-(-\Delta)^\alpha,\ \alpha\in(0,1]$, generalized $\rm
Schr\ddot{o}dinger$ operators, i.e. $L=\Delta+2\frac{\nabla
\rho}{\rho}\cdot\nabla$, and Laplacians on fractals.

33
The categories of this paper are: plasm-ph
30
The categories of this paper are: q-alg
4
The categories of this paper are: cond-mat
20
The categories of this paper are: acc-phys
14
The categories of this paper are: math-ph
32
The categories of this paper are: atom-ph
31
The categories of this paper are: ao-sci
10
The categories of this paper are: q-bio
12
The categories of this paper are: nucl-th
0
The categories of this paper are: hep-ph
1
The categories of this paper are: cs
22
The categories of this paper are: chao-dyn
18
The categories of this paper are: econ
29
The categories of this paper are: funct-an
11
The categories of this paper are: hep-lat
25
The categories of this paper are: patt-sol