Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Global existence for a class of reaction-diffusion systems with mass
  action kinetics and concentration-dependent diffusivities   In this work we study the existence of classical solutions for a class of
reaction-diffusion systems with quadratic growth naturally arising in mass
action chemistry when studying networks of reactions of the type $A_i+A_j
\rightleftharpoons A_k$ with Fickian diffusion, where the diffusion
coefficients might depend on time, space and on all the concentrations $c_i$ of
the chemical species. In the case of one single reaction, we prove global
existence for space dimensions $N\leq 5$. In the more restrictive case of
diffusion coefficients of the type $d_i(c_i)$, we use an $L^2$-approach to
prove global existence for $N\leq 9$. In the general case of networks of such
reactions we extend the previous method to get global solutions for general
diffusivities if $N\leq 3$ and for diffusion of type $d_i(c_i)$ if $N\leq 5$.
In the latter quasi-linear case of $d_i(c_i)$ and for space dimensions $N=2$
and $N=3$, global existence holds for more than quadratic reactions. We can
actually allow for more general rate functions including fractional power
terms, important in applications. We obtain global existence under appropriate
growth restrictions with an explicit dependence on the space dimension $N$.

24
The categories of this paper are: dg-ga
37
The categories of this paper are: supr-con
0
The categories of this paper are: hep-ph
33
The categories of this paper are: plasm-ph
6
The categories of this paper are: astro-ph
21
The categories of this paper are: adap-org
15
The categories of this paper are: nucl-ex
1
The categories of this paper are: cs
4
The categories of this paper are: cond-mat
30
The categories of this paper are: q-alg
29
The categories of this paper are: funct-an
12
The categories of this paper are: nucl-th
31
The categories of this paper are: ao-sci
35
The categories of this paper are: mtrl-th
23
The categories of this paper are: solv-int
19
The categories of this paper are: eess