Electron. J. Diff. Eqns., Vol. 1999(1999), No. 32, pp. 122.
The fundamental solution for a consistent complex model
of the shallow shell equations
Matthew P. Coleman
Abstract:
The calculation of the Fourier transforms of the fundamental solution in
shallow shell theory ostensibly was accomplished by J. L. Sanders
[J. Appl. Mech. 37 (1970), 361366]. However, as is shown in detail in this
paper, the complex model used by Sanders is, in fact, inconsistent.
This paper provides a consistent version of Sanders's complex model,
along with the Fourier transforms of the fundamental solution for this
corrected model. The inverse Fourier transforms are then calculated for the
particular cases of the shallow spherical and circular cylindrical shells, and
the results of the latter are seen to be in agreement with results
appearing elsewhere in the literature.
Submitted June 9, 1999. Published September 9, 1999.
Math Subject Classifications: 35Q72, 35A08, 73K15, 42B10.
Key Words: shallow shell theory, fundamental solution, spherical shell,
cylindrical shell.
Show me the
PDF file (172K),
TEX file, and other files for this article.

Matthew P. Coleman
Department of Mathematics and Computer Science
Fairfield University
Fairfield, CT 06430, U.S.A.
email: mcoleman@fair1.fairfield.edu 
Return to the EJDE web page