Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Verigin problem with and without phase transition   Isothermal compressible two-phase flows with and without phase transition are
modeled, employing Darcy's and/or Forchheimer's law for the velocity field. It
is shown that the resulting systems are thermodynamically consistent in the
sense that the available energy is a strict Lyapunov functional. In both cases,
the equilibria are identified and their thermodynamical stability is
investigated by means of a variational approach. It is shown that the problems
are well-posed in an $L_p$-setting and generate local semiflows in the proper
state manifolds. It is further shown that a non-degenerate equilibrium is
dynamically stable in the natural state manifold if and only if it is
thermodynamically stable. Finally, it is shown that a solution which does not
develop singularities exists globally and converges to an equilibrium in the
state manifold.

22
The categories of this paper are: chao-dyn
9
The categories of this paper are: nlin
8
The categories of this paper are: hep-ex
3
The categories of this paper are: physics
17
The categories of this paper are: q-fin
21
The categories of this paper are: adap-org
5
The categories of this paper are: gr-qc
30
The categories of this paper are: q-alg
4
The categories of this paper are: cond-mat
24
The categories of this paper are: dg-ga
13
The categories of this paper are: quant-ph
27
The categories of this paper are: comp-gas
34
The categories of this paper are: chem-ph
32
The categories of this paper are: atom-ph
15
The categories of this paper are: nucl-ex
19
The categories of this paper are: eess