Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Convex Sobolev inequalities related to unbalanced optimal transport   We study the behaviour of various Lyapunov functionals (relative entropies)
along the solutions of a family of nonlinear drift-diffusion-reaction equations
coming from statistical mechanics and population dynamics. These equations can
be viewed as gradient flows over the space of Radon measures equipped with the
Hellinger-Kantorovich distance. The driving functionals of the gradient flows
are not assumed to be geodesically convex or semi-convex. We prove new
isoperimetric-type functional inequalities, allowing us to control the relative
entropies by their productions, which yields the exponential decay of the
relative entropies.

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The categories of this paper are: nucl-th
30
The categories of this paper are: q-alg
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The categories of this paper are: adap-org
33
The categories of this paper are: plasm-ph
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The categories of this paper are: solv-int
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The categories of this paper are: acc-phys
3
The categories of this paper are: physics
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The categories of this paper are: stat
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The categories of this paper are: funct-an
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The categories of this paper are: supr-con
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The categories of this paper are: quant-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: comp-gas
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The categories of this paper are: ao-sci
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The categories of this paper are: math-ph