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We investigate the long-time behaviour of solutions to the Korteweg-de Vries equation with a zero order dissipation and an additional forcing term, when the space variable varies over , and prove that it is described by a maximal compact attractor in .
are bacteria that make strikingly regular spatial-temporal patterns on agar surfaces.
In this paper we investigate a mathematical model that has been
shown to display these structures when solved numerically. The model consists of an ordinary
differential equation coupled with a partial differential equation involving a first-order
hyperbolic aging term together with nonlinear degenerate diffusion. The system is shown to
admit global weak solutions.
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