A remark on the uniqueness of fundamental solutions to the -Laplacian equation, .
Compact attractor for weakly damped driven Korteweg-de Vries equations on the real line
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 .
An Age and Spatially Structured Population Model for Swarm-Colony Development
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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