Abstract
The short time existence of the unsteady free boundary appearing in the porous media is discussed by use of Nash-Moser's implicit function theorem. The uniqueness, existence and the semibounded estimates for the solution of the linearized equation play an important role in the proof of the existence theorem. Also Nash-Moser's implicit function theorem is modified in an applicable form.
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Kawarada, H., Koshigoe, H. Unsteady flow in porous media with a free surface. Japan J. Indust. Appl. Math. 8, 41–84 (1991). https://doi.org/10.1007/BF03167185
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DOI: https://doi.org/10.1007/BF03167185