Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Continuity Equations in Space-time Domains   In this paper we consider a class of continuity equations that are
conditioned to stay in general space-time domains, which is formulated as a
continuum limit of interacting particle systems. Firstly, we study the
well-posedness of the solutions and provide examples illustrating that the
stability of solutions is strongly related to the decay of initial data at
infinity. In the second part, we consider the vanishing viscosity approximation
of the system, given with the co-normal boundary data. If the domain is
spatially convex, the limit coincides with the solution of our original system,
giving another interpretation to the equation.

33
The categories of this paper are: plasm-ph
36
The categories of this paper are: cmp-lg
13
The categories of this paper are: quant-ph
23
The categories of this paper are: solv-int
14
The categories of this paper are: math-ph
34
The categories of this paper are: chem-ph
22
The categories of this paper are: chao-dyn
17
The categories of this paper are: q-fin
37
The categories of this paper are: supr-con
6
The categories of this paper are: astro-ph
31
The categories of this paper are: ao-sci
16
The categories of this paper are: stat
30
The categories of this paper are: q-alg
19
The categories of this paper are: eess
8
The categories of this paper are: hep-ex
21
The categories of this paper are: adap-org