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arXiv · 1705.02112

Global attractors for the Benjamin-Bona-Mahony equation with memory

Filippo Dell'Oro·Olivier Goubet·Youcef Mammeri·Vittorino Pata
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Abstract

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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Filippo Dell'Oro, Olivier Goubet, Youcef Mammeri, Vittorino Pata. 2017-05-05. Global attractors for the Benjamin-Bona-Mahony equation with memory. https://arxiv.org/abs/1705.02112

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