Extinction of a bacterial colony under forced convection in pie geometry

The extinction of a bacterial colony, as it is forced to migrate into a hostile environment, is analyzed in pie geometry. Under convection, separation of the radial and the azimuthal degrees of freedom is not possible, so the linearized evolution operator is diagonalized numerically. Some characteristic scales are compared with the results of recent experiments, and the "integrable" limit of the theory in the narrow growth region is studied.