Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Heat equation for weighted Banach space valued function spaces   We study the homogeneous equation (*) $ u' = \Delta u$, $t > 0$, $u(0)=f\in
wX$, where $wX$ is a weighted Banach space, $w(x)= (1+||x||)^k$, $x\in \r^n$
with $k\ge 0$, $ \Delta$ is the Laplacian, $Y$ a complex Banach space and $X$
one of the spaces $ BUC (\r^n,Y)\} $, $ C_0 (\r^n,Y)$, $ L^p (\r^n,Y)$, $1 \le
p < \infty$. It is shown that the mild solutions of (*) are still given by the
classical Gauss-Poisson formula, a holomorphic $C_0$-semigroup.

21
The categories of this paper are: adap-org
5
The categories of this paper are: gr-qc
6
The categories of this paper are: astro-ph
33
The categories of this paper are: plasm-ph
14
The categories of this paper are: math-ph
31
The categories of this paper are: ao-sci
3
The categories of this paper are: physics
1
The categories of this paper are: cs
12
The categories of this paper are: nucl-th
25
The categories of this paper are: patt-sol
34
The categories of this paper are: chem-ph
35
The categories of this paper are: mtrl-th
24
The categories of this paper are: dg-ga
30
The categories of this paper are: q-alg
27
The categories of this paper are: comp-gas
16
The categories of this paper are: stat