Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Existence and convexity of solutions of the fractional heat equation   We prove that the initial-value problem for the fractional heat equation
admits a solution provided that the (possibly unbounded) initial datum has a
conveniently moderate growth at infinity. Under the same growth condition we
also prove that the solution is unique. Our result does not require any sign
assumption, thus complementing the Widder's type theorem of Barrios et al.
(Arch. Rational Mech. Anal. 213 (2014) 629-650) for positive solutions.
Finally, we show that the fractional heat flow preserves convexity of the
initial datum. Incidentally, several properties of stationary convex solutions
are established.

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The categories of this paper are: nucl-ex
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The categories of this paper are: q-alg
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The categories of this paper are: nlin
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The categories of this paper are: nucl-th
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The categories of this paper are: alg-geom
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The categories of this paper are: chem-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: cond-mat
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The categories of this paper are: bayes-an
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The categories of this paper are: acc-phys
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The categories of this paper are: cs
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The categories of this paper are: patt-sol
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The categories of this paper are: supr-con
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The categories of this paper are: plasm-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: solv-int