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math.AP2022
Traveling wave solutions to the one-phase Muskat problem: existence and stability
Huy Q. Nguyen, Ian Tice
We study the Muskat problem for one fluid in arbitrary dimension, bounded below by a flat bed and above by a free boundary given as a graph. In addition to a fixed uniform gravitat…
math.AP2022
Coercivity of the Dirichlet-to-Neumann operator and applications to the Muskat problem
Huy Q. Nguyen
We consider the Dirichlet-to-Neumann operator in strip-like and half-space domains with Lipschitz boundary. It is shown that the quadratic form generated by the Dirichlet-to-Neuman…