2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/145533Proteus 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.Populations and EvolutionAnalysis of PDEs35M10; 35K65; 92D25text