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

Fahuai Yi

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 = {Fahuai Yi }, 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} }
TY - JOUR T1 - Local Classical Solution of Muskat Free Boundary Problem AU - Fahuai Yi JO - Journal of Partial Differential Equations VL - 1 SP - 84 EP - 96 PY - 1996 DA - 1996/09 SN - 9 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jpde/5611.html KW - Classical solution KW - Muskat problem KW - Newton's iteration method AB - 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.
Fahuai Yi . (1996). Local Classical Solution of Muskat Free Boundary Problem. Journal of Partial Differential Equations. 9 (1). 84-96. doi:
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