singular Perturbation Problems in Ship Hydrodynamics 



F'{z) (or $(x,y)), that is, the surface disturbance far away is a 

 real wave, but its shape and size depend only on the solution of the 

 rigid- wall problem. This is not true of the wave disturbance in the 

 vicinity of the body. 



It would be very useful, I am sure, to formulate this problem 

 carefully by the method of multi- scale expansions. The approach 

 described by Ogilvie [ 1968] is very heuristic and leaves much to be 

 desired. 



ACKNOWLEDGMENT 



The preparation of this paper was supported by a grant of the 

 National Science Foundation (Grant GK 14375). 



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Cole, Julian D. , Perturbation Methods in Applied Mathematics , 

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Dagan, G.,and Tulin, M. P., Bow Waves Before Blunt Ships, 

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Fedyayevskiy , K. Ko,and Sobolev, G. V. , Control and Stability in 

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