Some uniqueness theorems for linear water waves
Authors:
Shih Liang Wen and M. S. K. Sastry
Journal:
Quart. Appl. Math. 40 (1982), 93-100
MSC:
Primary 76B15; Secondary 35Q20
DOI:
https://doi.org/10.1090/qam/652053
MathSciNet review:
652053
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Abstract: Uniqueness theorems, under less restrictive conditions at infinity, for water of uniform finite depth, for the cliff problem and for waves on uniform sloping beaches are proved using the Phragmén-Lindelöf principle.
A. Weinstein, Sur un problème aux limits dans une bande indéfinie, C. R. Acad. Sci. Paris, 184, 497 (1927)
- J. J. Stoker, Water waves: The mathematical theory with applications, Pure and Applied Mathematics, Vol. IV, Interscience Publishers, Inc., New York; Interscience Publishers Ltd., London, 1957. MR 0103672
- Alexander Weinstein, On surface waves, Canad. J. Math. 1 (1949), 271–278. MR 30865, DOI https://doi.org/10.4153/cjm-1949-023-x
- Hans Lewy, Water waves on sloping beaches, Bull. Amer. Math. Soc. 52 (1946), 737–775. MR 22134, DOI https://doi.org/10.1090/S0002-9904-1946-08643-7
- J. J. Stoker, Surface waves in water of variable depth, Quart. Appl. Math. 5 (1947), 1–54. MR 22135, DOI https://doi.org/10.1090/S0033-569X-1947-22135-3
- Arthur S. Peters, Water waves over sloping beaches and the solution of a mixed boundary value problem for $\Delta ^2\phi -k^2\phi =0$ in a sector, Comm. Pure Appl. Math. 5 (1953), 87–108. MR 46807, DOI https://doi.org/10.1002/cpa.3160050103
- Maurice Roseau, Contribution à la théorie des ondes liquides de gravité en profondeur variable, Publ. Sci. Tech. Ministère de l’Air, Paris 1952 (1952), no. 275, ii+91 (French). MR 60965
- Murray H. Protter and Hans F. Weinberger, Maximum principles in differential equations, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1967. MR 0219861
- Shih-liang Wen, On a uniqueness theorem for linear gravity waves simple harmonic in time, Z. Angew. Math. Mech. 52 (1972), 178–179. MR 300540, DOI https://doi.org/10.1002/zamm.19720520309
A. Weinstein, Sur un problème aux limits dans une bande indéfinie, C. R. Acad. Sci. Paris, 184, 497 (1927)
J. J. Stoker, Water waves, Interscience Publishers, New York (1957)
A. Weinstein, On surface waves, Canadian J. Math. 1, 271 (1949)
H. Lewy, Water waves on sloping beaches, Bull. Amer. Math. Soc. 52, 737 (1946)
J. J. Stoker, Surface waves in water of variable depth, Quart. Appl. Math. 5, 1 (1947)
A. S. Peters, Water waves over sloping beaches and the solution of a mixed boundary value problem for $\Delta \phi - {k^2}\phi = 0$ in a sector, Comm. Pure Appl. Math. 5, 87 (1952)
M. Roseau, Contribution à la théorie des ondes liquides de gravité en profondeur variable, Publications Sci. Tech. du Ministere de l’Air, No. 275, Paris (1952)
M. H. Protter and H. F. Weinberger, Maximum principles in differential equations, Prentice-Hall, N. J., (1967)
S. Wen, On a uniqueness theorem for linear gravity waves simple harmonic in time, ZAMM 52, 178 (1972)
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Article copyright:
© Copyright 1982
American Mathematical Society
