TY - JOUR T1 - Local Classical Solution of Muskat Free Boundary Problem 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.