Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sharp interface limit of a non-mass-conserving Cahn--Hilliard system
  with source terms and non-solenoidal Darcy flow   We study the sharp interface limit of a non-mass-conserving
Cahn--Hilliard--Darcy system with the weak compactness method developed in Chen
(J. Differential Geometry, 1996). The source term present in the Cahn--Hilliard
component is a product of the order parameter and a prescribed function with
zero spatial mean, leading to non-conservation of mass. Furthermore, the
divergence of the velocity field is given by another prescribed function with
zero spatial mean, which yields a coupling of the Cahn--Hilliard equation to a
non-solenoidal Darcy flow. New difficulties arise in the derivation of uniform
estimates due to the presence of the source terms, which can be circumvented if
we consider the above specific structures. Moreover, due to the lack of
mass-conservation, the analysis is valid as long as one phase does not vanish
completely, leading to a local-in-time result. The sharp interface limit for a
Cahn--Hilliard--Brinkman system is also discussed.

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The categories of this paper are: eess
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The categories of this paper are: cs
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The categories of this paper are: ao-sci
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The categories of this paper are: solv-int
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The categories of this paper are: stat
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The categories of this paper are: alg-geom
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The categories of this paper are: supr-con
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The categories of this paper are: chem-ph
33
The categories of this paper are: plasm-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-th
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The categories of this paper are: cmp-lg
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The categories of this paper are: funct-an
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The categories of this paper are: math-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: mtrl-th