Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Scalar conservation laws with stochastic discontinuous flux function   A variety of real-world applications are modeled via hyperbolic conservation
laws. To account for uncertainties or insufficient measurements, random
coefficients may be incorporated. These random fields may depend
discontinuously on the state space, e.g., to represent permeability in a
heterogeneous or fractured medium. We introduce a suitable admissibility
criterion for the resulting stochastic discontinuous-flux conservation law and
prove its well-posedness. Therefore, we ensure the pathwise existence and
uniqueness of the corresponding deterministic setting and present a novel proof
for the measurability of the solution, since classical approaches fail in the
discontinuous-flux case. As an example of the developed theory, we present a
specific advection coefficient, which is modeled as a sum of a continuous
random field and a pure jump field. This random field is employed in the
stochastic conservation law, in particular a stochastic Burgers' equation, for
numerical experiments. We approximate the solution to this problem via the
Finite Volume method and introduce a new meshing strategy that accounts for the
resulting standing wave profiles caused by the flux-discontinuities. The
ability of this new meshing method to reduce the sample-wise variance is
demonstrated in numerous numerical investigations.

11
The categories of this paper are: hep-lat
20
The categories of this paper are: acc-phys
34
The categories of this paper are: chem-ph
23
The categories of this paper are: solv-int
8
The categories of this paper are: hep-ex
22
The categories of this paper are: chao-dyn
14
The categories of this paper are: math-ph
3
The categories of this paper are: physics
33
The categories of this paper are: plasm-ph
30
The categories of this paper are: q-alg
35
The categories of this paper are: mtrl-th
17
The categories of this paper are: q-fin
13
The categories of this paper are: quant-ph
15
The categories of this paper are: nucl-ex
9
The categories of this paper are: nlin
31
The categories of this paper are: ao-sci