Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Decay rates for a class of diffusive-dominated interaction equations   We analyse qualitative properties of the solutions to a mean-field equation
for particles interacting through a pairwise potential while diffusing by
Brownian motion. Interaction and diffusion compete with each other depending on
the character of the potential. We provide sufficient conditions on the
relation between the interaction potential and the initial data for diffusion
to be the dominant term. We give decay rates of Sobolev norms showing that
asymptotically for large times the behavior is then given by the heat equation.
Moreover, we show an optimal rate of convergence in the $L^1$-norm towards the
fundamental solution of the heat equation.

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The categories of this paper are: supr-con
6
The categories of this paper are: astro-ph
23
The categories of this paper are: solv-int
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The categories of this paper are: comp-gas
8
The categories of this paper are: hep-ex
19
The categories of this paper are: eess
10
The categories of this paper are: q-bio
34
The categories of this paper are: chem-ph
14
The categories of this paper are: math-ph
35
The categories of this paper are: mtrl-th
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The categories of this paper are: dg-ga
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The categories of this paper are: stat
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The categories of this paper are: q-fin
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The categories of this paper are: q-alg
5
The categories of this paper are: gr-qc
9
The categories of this paper are: nlin