Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

  • [1] A. Weinstein, Sur un problème aux limits dans une bande indéfinie, C. R. Acad. Sci. Paris, 184, 497 (1927)
  • [2] J. J. Stoker, Water waves, Interscience Publishers, New York (1957) MR 0103672
  • [3] A. Weinstein, On surface waves, Canadian J. Math. 1, 271 (1949) MR 0030865
  • [4] H. Lewy, Water waves on sloping beaches, Bull. Amer. Math. Soc. 52, 737 (1946) MR 0022134
  • [5] J. J. Stoker, Surface waves in water of variable depth, Quart. Appl. Math. 5, 1 (1947) MR 0022135
  • [6] 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) MR 0046807
  • [7] 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) MR 0060965
  • [8] M. H. Protter and H. F. Weinberger, Maximum principles in differential equations, Prentice-Hall, N. J., (1967) MR 0219861
  • [9] S. Wen, On a uniqueness theorem for linear gravity waves simple harmonic in time, ZAMM 52, 178 (1972) MR 0300540

Similar Articles

Retrieve articles in Quarterly of Applied Mathematics with MSC: 76B15, 35Q20

Retrieve articles in all journals with MSC: 76B15, 35Q20

Additional Information

DOI: https://doi.org/10.1090/qam/652053
Article copyright: © Copyright 1982 American Mathematical Society

American Mathematical Society