Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Darcy's Law with a Source term   We introduce a novel variant of the JKO scheme to approximate Darcy's law
with a pressure dependent source term. By introducing a new variable that
implicitly controls the source term, our scheme is still able to use the
standard Wasserstein-2-metric even though the total mass changes over time.
Leveraging the dual formulation of our scheme, we show that the
discrete-in-time approximations satisfy many useful properties expected for the
continuum solutions, such as a comparison principle and uniform
$L^1$-equicontinuity. Many of these properties are new even in the
well-understood case where the growth term is absent. Finally, we show that our
discrete approximations converge to a solution of the corresponding PDE system,
including a tumor growth model with a general nonlinear source term.

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The categories of this paper are: astro-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: q-bio
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The categories of this paper are: solv-int
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The categories of this paper are: nucl-th
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The categories of this paper are: q-alg
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The categories of this paper are: eess
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The categories of this paper are: nlin
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The categories of this paper are: hep-th
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The categories of this paper are: chem-ph
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The categories of this paper are: q-fin
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The categories of this paper are: atom-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: funct-an