I h 



h(x,t) _T - r 



dzdt = 



L 



[!M 



h(x,t) 



z - (})(z=h) h. 



dxdt 



r h(x,t) 



-J J '*. -} 



dt 4>(z=h) h 







dx 



J Jj *t dzdxdt " -J 



D 1 (t) 



h ())dxdt + | | c|)dxdz 



S US^ D. (t=T) 



s F 1 



\\ 



(8) 



Now we take a variation of J in Equation (6) , and use the Green theorem, and the 

 condition at large t = 1 obtaining 



Jj (l V *l vV»it + s h ) 



0S 1F 



5h dxdt 



V<J> 5tj> dzdxdt 



D, 



-n 



s._.us 



IF s 



>, /h +1 -h 6(f), dxdt 

 in x t / 1 



J J (* ln ^ 2n ) 6^ dzdt -J J ( V * 2 ) 

 OS, o S T 



2n 



dzdt 



•if J 



S. 



2 T 2n r 2 T 2n 



) dzdt = 



(9) 



However from the identity, 



