On certain boundary-value problems with strong vanishing on the boundary
Authors:
J. McCrea and J. L. Synge
Journal:
Quart. Appl. Math. 24 (1967), 355-364
MSC:
Primary 53.45; Secondary 35.00
DOI:
https://doi.org/10.1090/qam/216414
MathSciNet review:
216414
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Abstract: In Newtonian statics of a continuum we have a symmetric stress tensor with six components and a body-force with three components, and the divergence of the stress tensor equals the body-force vector reversed. If the body-force vector as assigned in some finite domain $I$ with boundary $B$, we have three equations to be satisfied by six stress components. The equations of equilibrium, coupled with conditions on $B$, cannot determine the stress, but they do define a class of stress distributions, provided the body-force and the conditions on $B$ are consistent. The purpose of this paper is to show that, if the body-force satisfies the usual conditions of equilibrium and vanishes strongly on $B$ in the sense that this body-force, and all its derivatives up to order $N$, vanish on $B$, then there exists a stress distribution which also vanishes strongly on $B$, the order of vanishing being greater by one than that of the body-force.
W. S. Dorn and A. Schild, Quart. Appl. Math. 14, 210, (1956)
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Article copyright:
© Copyright 1967
American Mathematical Society