An Age and Spatially Structured Population Model forProteus MirabilisSwarm-Colony Development

Abstract

Abstract. Proteus mirabilis 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.

Structured models of cell migration incorporating molecular binding processes

“…The diffusive flux term in ( 12) is chosen as −D c ∇ x c. The same form is used, for instance, in the work of Laurençot and Walker (2008), who consider an age-structured spatio-temporal model for proteus mirabilis swarm-colony development. This form implies that the random motility of cells with a particular i-state y depends only on the gradient of the density of cells having that same i-state.…”

Nonlocal hyperbolic population models structured by size and spatial position: Well-posedness

“…Many population models consider the values of the time-dependent density in the Lebesgue-Bochner space L 1 ([s min , s max ]; Y ) where Y denotes a real Banach space of functions defined on R (see, e.g., [7,8,13,33,52,68,85] and references therein). This rearrangement of variables opens the door to semigroup approaches (with linear or nonlinear operators in Banach spaces, see, e.g., [35,36,37,38,55,75,76,87,88,89] and references therein).…”

A mathematical model for continuous crystallization

“…A similar line is chosen in an epidemic model treated by Lanelli , and for tumor growth by Perthame . Laurençot and Walker use an approach by weak solutions for a model of infectious diseases.…”