Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Homogenization of parabolic problems with dynamical boundary conditions
  of reactive-diffusive type in perforated media   This paper deals with the homogenization of the reaction-diffusion equations
in a domain containing periodically distributed holes of size $\varepsilon$,
with a dynamical boundary condition of reactive-diffusive type, i.e., we
consider the following nonlinear boundary condition on the surface of the holes
$$ \nabla u_\varepsilon \cdot \nu+\varepsilon\,\displaystyle\frac{\partial
u_\varepsilon}{\partial t}=\varepsilon\,\delta
\Delta_{\Gamma}u_\varepsilon-\varepsilon\,g(u_\varepsilon), $$ where
$\Delta_{\Gamma}$ denotes the Laplace-Beltrami operator on the surface of the
holes, $\nu$ is the outward normal to the boundary, $\delta>0$ plays the role
of a surface diffusion coefficient and $g$ is the nonlinear term. We generalize
our previous results (see [3]) established in the case of a dynamical boundary
condition of pure-reactive type, i.e., with $\delta=0$. We prove the
convergence of the homogenization process to a nonlinear reaction-diffusion
equation whose diffusion matrix takes into account the reactive-diffusive
condition on the surface of the holes.

17
The categories of this paper are: q-fin
22
The categories of this paper are: chao-dyn
34
The categories of this paper are: chem-ph
12
The categories of this paper are: nucl-th
31
The categories of this paper are: ao-sci
1
The categories of this paper are: cs
16
The categories of this paper are: stat
28
The categories of this paper are: alg-geom
37
The categories of this paper are: supr-con
35
The categories of this paper are: mtrl-th
0
The categories of this paper are: hep-ph
7
The categories of this paper are: hep-th
23
The categories of this paper are: solv-int
32
The categories of this paper are: atom-ph
24
The categories of this paper are: dg-ga
10
The categories of this paper are: q-bio