| Abstract: |
| The Hele-Shaw problem models the dynamics of the interface of a single viscous fluid domain in porous media. While the dynamics around a corner on the fluid interface are known in the absence of surface tension, less is known with the presence of surface tension. We demonstrate the existence of self-similar solutions that initially have a corner, but instantaneously smoothen out. Due to surface tension, the differential equation describing the self-similar solution is a third order nonlocal equation of elliptic type with coefficients that grow at infinity, and thus, requires an interesting linear analysis. |
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