By J. Talbert, H. Heng

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11) with dSO/dt P(d60/dt) + (1 - p)a (a) where ay is a mollification of a(a). 20) by merely regarding these coefficients of It 6 ) 0 and the associated choosing I > TO of the above steps we have the following. y sufficiently are satisfied. linearized small. Fur- By summarizing all teger. 1) u + n u n Sn First, we introduce + + v o + n U - o + vn U So + n 0, 1, 2, ... 5) T]. conventional 2 T s ,n , 2 s,n , _ M a (¢)2 s+l,n,T x (_00, 00) + s = T Ma x n± x (_00, "j + 2 ClnJ s-j locally to the norms cor- +00 and also we de- Sobolev norms of order L (~) j=a a by regions and M higher derivative etc.

18). 11) with dSO/dt P(d60/dt) + (1 - p)a (a) where ay is a mollification of a(a). 20) by merely regarding these coefficients of It 6 ) 0 and the associated choosing I > TO of the above steps we have the following. y sufficiently are satisfied. linearized small. Fur- By summarizing all teger. 1) u + n u n Sn First, we introduce + + v o + n U - o + vn U So + n 0, 1, 2, ... 5) T]. conventional 2 T s ,n , 2 s,n , _ M a (¢)2 s+l,n,T x (_00, 00) + s = T Ma x n± x (_00, "j + 2 ClnJ s-j locally to the norms cor- +00 and also we de- Sobolev norms of order L (~) j=a a by regions and M higher derivative etc.

Y sufficiently are satisfied. linearized small. Fur- By summarizing all teger. 1) u + n u n Sn First, we introduce + + v o + n U - o + vn U So + n 0, 1, 2, ... 5) T]. conventional 2 T s ,n , 2 s,n , _ M a (¢)2 s+l,n,T x (_00, 00) + s = T Ma x n± x (_00, "j + 2 ClnJ s-j locally to the norms cor- +00 and also we de- Sobolev norms of order L (~) j=a a by regions and M higher derivative etc. 1. (v+, v-, where cRO . 5). 8) n+1 - 1 -L±(u±, n and choose + v~+1 , n = 0, 1, 2, ... tO the + L (u + + n , Bn )v n +1 For defining the iteration like to find (a, t) u+, u-, B E MO x [0, T] nonlinear equation, scheme on the boundary, so that the nonlinear for sufficiently G(w) = O.

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