We study a singular perturbation problem for a certain type of reaction diiusion equation with a space-dependent reaction term. We compare the eeect that the presence of boundary layers versus internal layers has on the existence and stability of stationary solutions. In particular, we show that the associated eigenvalues are of diierent orders of magnitude for the two kinds of layers.

The Primitive Equations of the ocean and the atmosphere are fundamental equations of geophysical fluid mechanics [10,15]. In the presence of viscosity, it has been shown—in various contexts—that these equations are well-posed (see e.g., [7,8], and the review article [14]). In the absence of viscosity, it is known that the PEs are not wellposed for any set of boundary conditions of local type. T...

Significant progress has been made towards understanding the large scale features of wall-bounded shear flow in zero pressure gradient (ZPG) turbulent boundary layers (TBL). Here we consider their effects in adverse pressure gradient (APG) flows where the pressure gradient parameter is held constant and Reynolds number is varied. This is done by documenting the changes in the mean velocity, str...

The influence of high levels of wall cooling on the stability of hypervelocity boundary layers is investigated. Such conditions are relevant to experiments in high-enthalpy impulse facilities, where the wall temperature is much smaller than the free-stream temperature, as well as to some real flight scenarios. Some effects of wall cooling are well known, for instance, the stabilization of the f...