On the Stefan type problems

The project aims to introduce novel ideas and different techniques to substantially develop further theories of generalized Stefan problems. More precisely, we will lay out the project in two directions. The main thrust of the first direction is to carefully examine the effect of the p-Laplacian operator on the two-phase transition. We will develop innovative approaches to sharpen the modulus of continuity for weak solutions, both in the interior and at the boundary of rough domains. Whereas the second direction focuses on multi-phase transitions. In particular, we will establish a regularity and existence theory for the saturation of two immiscible fluids in a porous medium, when connate water is present. The effort will shed light on long term goals of treating very general multi-phase problems.
The project aims to introduce novel ideas and different techniques to substantially develop further theories of generalized Stefan problems. More precisely, we will lay out the project in two directions. The main thrust of the first direction is to carefully examine the effect of the p-Laplacian operator on the two-phase transition. We will develop innovative approaches to sharpen the modulus of continuity for weak solutions, both in the interior and at the boundary of rough domains. Whereas the second direction focuses on multi-phase transitions. In particular, we will establish a regularity and existence theory for the saturation of two immiscible fluids in a porous medium, when connate water is present. The effort will shed light on long term goals of treating very general multi-phase problems.