Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Well-posedness and regularity of the Cauchy problem for nonlinear
  fractional in time and space equations   The purpose is to study the Cauchy problem for non-linear in time and space
pseudo-differential equations. These include the fractional in time versions of
HJB equations governing the controlled scaled CTRW. As a preliminary step which
is of independent interest we analyse the corresponding linear equation proving
its well-posedness and smoothing properties.

31
The categories of this paper are: ao-sci
37
The categories of this paper are: supr-con
12
The categories of this paper are: nucl-th
11
The categories of this paper are: hep-lat
7
The categories of this paper are: hep-th
15
The categories of this paper are: nucl-ex
21
The categories of this paper are: adap-org
16
The categories of this paper are: stat
25
The categories of this paper are: patt-sol
14
The categories of this paper are: math-ph
33
The categories of this paper are: plasm-ph
9
The categories of this paper are: nlin
13
The categories of this paper are: quant-ph
0
The categories of this paper are: hep-ph
28
The categories of this paper are: alg-geom
10
The categories of this paper are: q-bio