Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Study of a fractional stochastic heat equation   In this article, we study a $d$-dimensional stochastic nonlinear heat
equation (SNLH) with a quadratic nonlinearity, forced by a fractional
space-time white noise: \begin{equation*} \left\{\begin{array}{l} \partial_t
u-\Delta u= \rho^2 u^2 + \dot B \, , \quad t\in [0,T] \, , \, x\in \mathbb{R}^d
\, ,\\ u_0=\phi\, . \end{array} \right. \end{equation*} Two types of regimes
are exhibited, depending on the ranges of the Hurst index $H=(H_0,...,H_d)$
$\in (0,1)^{d+1}$. In particular, we show that the local well-posedness of
(SNLH) resulting from the Da Prato-Debussche trick, is easily obtained when $2
H_0+\sum_{i=1}^{d}H_i >d$. On the contrary, (SNLH) is much more difficult to
handle when $2H_0+\sum_{i=1}^{d}H_i \leq d$. In this case, the model has to be
interpreted in the Wick sense, thanks to a time-dependent renormalization.
Helped with the regularising effect of the heat semigroup, we establish local
well-posedness results for (SNLH) for all dimension $d\geq1.$

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The categories of this paper are: funct-an
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The categories of this paper are: atom-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: cmp-lg
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The categories of this paper are: cond-mat
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The categories of this paper are: chem-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: alg-geom
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The categories of this paper are: quant-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: gr-qc
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The categories of this paper are: patt-sol
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The categories of this paper are: physics
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The categories of this paper are: cs
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The categories of this paper are: bayes-an
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The categories of this paper are: q-alg