Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Ergodicity of a nonlinear stochastic reaction-diffusion equation with
  memory   We consider a class of semi-linear differential Volterra equations with
memory terms, polynomial nonlinearities and random perturbation. For a broad
class of nonlinearities, we study statistically steady states of the system and
find that they possess regularities compatible with those of the weak
solutions. Moreover, if sufficiently many directions in the phase space are
stochastically forced, we employ the \emph{generalized coupling} approach to
establish the existence and uniqueness of the invariant probability measure to
which the system is exponentially attractive. This extends ergodicity results
previously established in [Bonaccorsi et al., SIAM J. Math. Anal., 44 (2012)].

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The categories of this paper are: cs
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The categories of this paper are: q-fin
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The categories of this paper are: plasm-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: math-ph
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The categories of this paper are: q-bio
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The categories of this paper are: gr-qc
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The categories of this paper are: nucl-th
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The categories of this paper are: stat
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The categories of this paper are: astro-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-th
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The categories of this paper are: solv-int
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The categories of this paper are: ao-sci
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The categories of this paper are: chem-ph