Volume 9, Issue 1
Local Classical Solution of Muskat Free Boundary Problem

Fahuai Yi

DOI:

J. Part. Diff. Eq., 9 (1996), pp. 84-96.

Published online: 1996-09

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  • Abstract

In this paper we consider the two-dimensional Muskat free boundary problem: Δu_i(x,t) = 0 in space-time domain Q_i (i = 1,2), here tis a parameter. The unknown surface Γ_pT (free boundary) is tltc common part of the boundaries of Q_1 and Q_2. The free boundary conditions are u_1(x,t) = u_2(x,t) and -k_1\frac{∂u_1}{∂n} = -k_2\frac{∂u_2}{∂n} = V_n. If the initial normal velocity of the free boundary is positive, we shall prove the existence of classical solution locally in time and uniqueness by making use of Newton's iteration method.

  • Keywords

Classical solution Muskat problem Newton's iteration method

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@Article{JPDE-9-84, author = {}, title = {Local Classical Solution of Muskat Free Boundary Problem}, journal = {Journal of Partial Differential Equations}, year = {1996}, volume = {9}, number = {1}, pages = {84--96}, abstract = { In this paper we consider the two-dimensional Muskat free boundary problem: Δu_i(x,t) = 0 in space-time domain Q_i (i = 1,2), here tis a parameter. The unknown surface Γ_pT (free boundary) is tltc common part of the boundaries of Q_1 and Q_2. The free boundary conditions are u_1(x,t) = u_2(x,t) and -k_1\frac{∂u_1}{∂n} = -k_2\frac{∂u_2}{∂n} = V_n. If the initial normal velocity of the free boundary is positive, we shall prove the existence of classical solution locally in time and uniqueness by making use of Newton's iteration method.}, issn = {2079-732X}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jpde/5611.html} }
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