Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Thin film evolution equations from (evaporating) dewetting liquid layers
  to epitaxial growth   In the present contribution we review basic mathematical results for three
physical systems involving self-organising solid or liquid films at solid
surfaces. The films may undergo a structuring process by dewetting,
evaporation/condensation or epitaxial growth, respectively. We highlight
similarities and differences of the three systems based on the observation that
in certain limits all of them may be described using models of similar form,
i.e., time evolution equations for the film thickness profile. Those equations
represent gradient dynamics characterized by mobility functions and an
underlying energy functional.
  Two basic steps of mathematical analysis are used to compare the different
system. First, we discuss the linear stability of homogeneous steady states,
i.e., flat films; and second the systematics of non-trivial steady states,
i.e., drop/hole states for dewetting films and quantum dot states in epitaxial
growth, respectively. Our aim is to illustrate that the underlying solution
structure might be very complex as in the case of epitaxial growth but can be
better understood when comparing to the much simpler results for the dewetting
liquid film. We furthermore show that the numerical continuation techniques
employed can shed some light on this structure in a more convenient way than
time-stepping methods.
  Finally we discuss that the usage of the employed general formulation does
not only relate seemingly not related physical systems mathematically, but does
as well allow to discuss model extensions in a more unified way.

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The categories of this paper are: acc-phys
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The categories of this paper are: atom-ph
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The categories of this paper are: q-fin
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The categories of this paper are: solv-int
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The categories of this paper are: hep-ex
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The categories of this paper are: q-bio
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The categories of this paper are: cs
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The categories of this paper are: quant-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: bayes-an
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The categories of this paper are: adap-org
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The categories of this paper are: ao-sci
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The categories of this paper are: econ
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The categories of this paper are: chao-dyn
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The categories of this paper are: comp-gas