Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: For the splitting method of the nonlinear heat equation with initial
  datum in W^1,q   In this paper, we analyze an operator splitting scheme of the nonlinear heat
equation in $\Omega\subset\mathbb{R}^d$ ($d\geq 1$): $\partial_t u = \Delta u +
\lambda |u|^{p-1} u$ in $\Omega\times(0,\infty)$, $u=0$ in
$\partial\Omega\times(0,\infty)$, $u ({\bf x},0) =\phi ({\bf x})$ in $\Omega$.
where $\lambda\in\{-1,1\}$ and $\phi \in W^{1,q}(\Omega)\cap L^{\infty}
(\Omega)$ with $2\leq p < \infty$ and $d(p-1)/2<q<\infty$. We establish the
well-posedness of the approximation of $u$ in $L^r$-space ($r\geq q$), and
furthermore, we derive its convergence rate of order $\mathcal{O}(\tau)$ for a
time step $\tau>0$. Finally, we give some numerical examples to confirm the
reliability of the analyzed result.

0
The categories of this paper are: hep-ph
15
The categories of this paper are: nucl-ex
18
The categories of this paper are: econ
26
The categories of this paper are: bayes-an
8
The categories of this paper are: hep-ex
24
The categories of this paper are: dg-ga
23
The categories of this paper are: solv-int
31
The categories of this paper are: ao-sci
34
The categories of this paper are: chem-ph
12
The categories of this paper are: nucl-th
14
The categories of this paper are: math-ph
29
The categories of this paper are: funct-an
9
The categories of this paper are: nlin
30
The categories of this paper are: q-alg
36
The categories of this paper are: cmp-lg
7
The categories of this paper are: hep-th