Geodesic
The fundamental solution for a consistent complex model of the shallow shell equations
Electronic journal of differential equations, Tome 1999 (1999)
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), 361-366]. 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.
Classification : 35Q72, 35A08, 73K15, 42B10
Keywords: shallow shell theory, fundamental solution, spherical shell, cylindrical shell 
@article{EJDE_1999__1999__a84,
     author = {Coleman,  Matthew P.},
     title = {The fundamental solution for a consistent complex model of the shallow shell equations},
     journal = {Electronic journal of differential equations},
     year = {1999},
     volume = {1999},
     zbl = {0924.35174},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_1999__1999__a84/}
}
TY  - JOUR
AU  - Coleman,  Matthew P.
TI  - The fundamental solution for a consistent complex model of the shallow shell equations
JO  - Electronic journal of differential equations
PY  - 1999
VL  - 1999
UR  - http://geodesic.mathdoc.fr/item/EJDE_1999__1999__a84/
LA  - en
ID  - EJDE_1999__1999__a84
ER  - 
%0 Journal Article
%A Coleman,  Matthew P.
%T The fundamental solution for a consistent complex model of the shallow shell equations
%J Electronic journal of differential equations
%D 1999
%V 1999
%U http://geodesic.mathdoc.fr/item/EJDE_1999__1999__a84/
%G en
%F EJDE_1999__1999__a84
Coleman,  Matthew P. The fundamental solution for a consistent complex model of the shallow shell equations. Electronic journal of differential equations, Tome 1999 (1999). http://geodesic.mathdoc.fr/item/EJDE_1999__1999__a84/