Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Blow-up time of strong solutions to a biological network formation model
  in high space dimensions   We investigate the possible blow-up of strong solutions to a biological
network formation model originally introduced by D. Cai and D. Hu \cite{HC}.
The model is represented by an initial boundary value problem for an
elliptic-parabolic system with cubic non linearity. We obtain an algebraic
equation for the possible blow-up time of strong solutions. The equation yields
information on how various given data may contribute to the blow-up of
solutions. As a by-product of our development, we establish a $W^{1,q}$
estimate for solutions to an elliptic equation which shows the explicit
dependence of the upper bound on the elliptic coefficients.

26
The categories of this paper are: bayes-an
34
The categories of this paper are: chem-ph
1
The categories of this paper are: cs
4
The categories of this paper are: cond-mat
36
The categories of this paper are: cmp-lg
19
The categories of this paper are: eess
15
The categories of this paper are: nucl-ex
16
The categories of this paper are: stat
35
The categories of this paper are: mtrl-th
11
The categories of this paper are: hep-lat
8
The categories of this paper are: hep-ex
24
The categories of this paper are: dg-ga
33
The categories of this paper are: plasm-ph
29
The categories of this paper are: funct-an
10
The categories of this paper are: q-bio
30
The categories of this paper are: q-alg