Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Degenerate parabolic equation with zero flux boundary condition and its
  approximations   We study a degenerate parabolic-hyperbolic equation with zero flux boundary
condition. The aim of this paper is to prove convergence of numerical
approximate solutions towards the unique entropy solution. We propose an
implicit finite volume scheme on admissible mesh. We establish fundamental
estimates and prove that the approximate solution converge towards an
entropy-process solution. Contrarily to the case of Dirichlet conditions, in
zero-flux problem unnatural boundary regularity of the flux is required to
establish that entropy-process solution is the unique entropy solution. In the
study of well-posedness of the problem, tools of nonlinear semigroup theory
(stationary, mild and integral solutions) were used in [Andreianov, Gazibo,
ZAMP, 2013] in order to overcome this difficulty. Indeed, in some situations
including the one-dimensional setting, solutions of the stationary problem
enjoy additional boundary regularity. Here, similar arguments are developed
based on the new notion of integral-process solution that we introduce for this
purpose.

33
The categories of this paper are: plasm-ph
17
The categories of this paper are: q-fin
24
The categories of this paper are: dg-ga
22
The categories of this paper are: chao-dyn
36
The categories of this paper are: cmp-lg
20
The categories of this paper are: acc-phys
28
The categories of this paper are: alg-geom
13
The categories of this paper are: quant-ph
14
The categories of this paper are: math-ph
31
The categories of this paper are: ao-sci
35
The categories of this paper are: mtrl-th
5
The categories of this paper are: gr-qc
16
The categories of this paper are: stat
37
The categories of this paper are: supr-con
27
The categories of this paper are: comp-gas
19
The categories of this paper are: eess