Long time regularity of solutions of the Hele–Shaw problem |
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Authors: | Inwon Kim |
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Institution: | Department of Mathematics, UCLA, USA |
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Abstract: | In this paper we study the long-time behavior of solutions of the one phase Hele–Shaw problem without surface tension. We show that after a finite time solutions of the Hele–Shaw problem become starshaped and Lipschitz continuous in space. Based on this observation we then prove that the free boundary become smooth in space and time with nondegenerate free boundary speed. |
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Keywords: | Viscosity solutions Free boundary Hele&ndash Show problem Long time behavior |
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