Solution of a system of nonlinear diffusion equations of porous medium type with exponent 2 leading to the formation of free boundaries and sharp fronts.

Free boundary and moving interface problems arise in Partial Differential Equations when, in addition to the basic unknown solution to the system of governing equations, the domain of the problem is itself a priori unknown. 

Free boundary problems are ubiquitous, and model a variety of physical phenomena, ranging from classical parabolic-type phase transition problems to hyperbolic-type multi-phase fluid flows, the latter playing a central role in a multitude of physical and engineering applications, ranging from the creation of hurricanes due to wind blowing on top of the ocean surface to the atomization of liquid fuel jets in combustion chambers to the motion of astrophysical bodies such as gaseous stars, and to fundamental predictions in atmospheric science and meteorology.

Faculty: José A. Carrillo and Gui-Qiang G. Chen

Postdoctoral Research Fellows: Difan Yuan

DPhil Students: Alex Cliffe

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