Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Boundedness of Classical Solutions to a Degenerate Keller--Segel Type
  Model with Signal-dependent Motilities   In this paper, we consider the initial Neumann boundary value problem for a
degenerate kinetic model of Keller--Segel type. The system features a
signal-dependent decreasing motility function that vanishes asymptotically,
i.e., degeneracies may take place as the concentration of signals tends to
infinity. In the present work, we are interested in the boundedness of
classical solutions when the motility function satisfies certain decay rate
assumptions. Roughly speaking, in the two-dimensional setting, we prove that
classical solution is globally bounded if the motility function decreases
slower than an exponential speed at high signal concentrations. In higher
dimensions, boundedness is obtained when the motility decreases at certain
algebraical speed. The proof is based on the comparison methods developed in
our previous work \cite{FJ19a,FJ19b} together with a modified Alikakos--Moser
type iteration. Besides, new estimations involving certain weighted energies
are also constructed to establish the boundedness.

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The categories of this paper are: eess
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The categories of this paper are: math-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-ph
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The categories of this paper are: supr-con
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The categories of this paper are: hep-th
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The categories of this paper are: econ
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The categories of this paper are: patt-sol
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The categories of this paper are: ao-sci
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The categories of this paper are: physics
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-ex
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The categories of this paper are: chem-ph
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The categories of this paper are: stat
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The categories of this paper are: atom-ph