Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Global attractors for the Benjamin-Bona-Mahony equation with memory   We consider the nonlinear integrodifferential Benjamin-Bona-Mahony equation
$$ u_t - u_{txx} + u_x - \int_0^\infty g(s) u_{xx}(t-s) {\rm d} s + u u_x = f
$$ where the dissipation is entirely contributed by the memory term. Under a
suitable smallness assumption on the external force $f$, we show that the
related solution semigroup possesses the global attractor in the natural weak
energy space. The result is obtained by means of a nonstandard approach based
on the construction of a suitable family of attractors on certain invariant
sets of the phase space.

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The categories of this paper are: dg-ga
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The categories of this paper are: nucl-th
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The categories of this paper are: comp-gas
6
The categories of this paper are: astro-ph
14
The categories of this paper are: math-ph
35
The categories of this paper are: mtrl-th
20
The categories of this paper are: acc-phys
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The categories of this paper are: hep-th
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The categories of this paper are: chao-dyn
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The categories of this paper are: bayes-an
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The categories of this paper are: gr-qc
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The categories of this paper are: solv-int
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The categories of this paper are: cmp-lg
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The categories of this paper are: cs
0
The categories of this paper are: hep-ph
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The categories of this paper are: q-fin