An integral equation formulation of the impedance bottom boundary condition for the parabolic wave equation

1980 ◽  
Vol 68 (S1) ◽  
pp. S51-S51
Author(s):  
John S. Papadakis ◽  
Ding Lee ◽  
George Botseas
Keyword(s):  
Boundary Condition ◽  
Integral Equation ◽  
Wave Equation ◽  
Bottom Boundary ◽  
Equation Formulation ◽  
Bottom Boundary Condition ◽  
Integral Equation Formulation

On periodic water-waves and their convergence to solitary waves in the long-wave limit

1981 ◽  
Vol 303 (1481) ◽  
pp. 633-669 ◽  
Keyword(s):  
Integral Equation ◽  
Solitary Waves ◽  
Water Waves ◽  
Periodic Problem ◽  
Existence Theory ◽  
Periodic Waves ◽  
Equation Formulation ◽  
Long Wave ◽  
Integral Equation Formulation ◽  
Wave Limit

A detailed discussion of Nekrasov’s approach to the steady water-wave problems leads to a new integral equation formulation of the periodic problem. This development allows the adaptation of the methods of Amick & Toland (1981) to show the convergence of periodic waves to solitary waves in the long-wave limit. In addition, it is shown how the classical integral equation formulation due to Nekrasov leads, via the Maximum Principle, to new results about qualitative features of periodic waves for which there has long been a global existence theory (Krasovskii 1961, Keady & Norbury 1978).

An integral equation formulation for the unconfined flow of groundwater with variable inlet conditions

1995 ◽  
Vol 18 (1) ◽  
pp. 15-36 ◽  
Author(s):  
Z. -X. Chen ◽  
G. S. Bodvarsson ◽  
P. A. Witherspoon ◽  
Y. C. Yortsos
Keyword(s):  
Integral Equation ◽  
Equation Formulation ◽  
Unconfined Flow ◽  
Integral Equation Formulation ◽  
Inlet Conditions
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