By Niçaise

Nicaise S. examine numerique et equations aux derivees partielles (Dunod, 2000)(fr)(ISBN 2100049410)

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M e c h . _26 (1962), p p . 9139 2 2 . T r a n s l a t i o n in J. Appl. M a t h , and M e c h . 2h_ (1962), p p . 1378-1392. 5. C a l l e g a r i , A. J. and R e i s s , E. L . , S h a l l o w S h e e t S n a p p i n g , in p r e p a r a t i o n . 6. Bromberg, E. and S t o k e r , J. J. , N o n - L i n e a r Theory of Curved E l a s t i c S h e e t s , Q . Appl. M a t h . _3 (1945), p p . 246-26 5. 7. M a r g u e r r e , K. , Zur t h e o r i e d e r gekrummten P l a t t e G r o s s e r F o r m a n d e r u n g , P r o c .

49 BERNARD D. 14) f e Ji, o < d(f, f°) < 6 => r 0O (f) > r0O(f°) . Proof. Let f in 21 be such that 0 < d(£, £°) < 6. 15) r G O (f) > r 0 D ( f t . ) . By item (B), we here have d(f ,, £°) < a. 15) yields r 0 O ( | ) >~r 0O (f°). ) > r 0 o(f°). d. Theorems 3, 4 , and 5 show that the energy criterion for stability has a dynamical significance in that it supplies a necessary condition for asymptotic stability. (£°, 0°) for which lim d(f t , f°) = 0 and for which f = f1 and 0(# , T) = 0 ° for all T < 0.

3) *(t) EE r e 0 ( f ° ) ; thus, in an equilibrium state the canonical free energy equals the equilibrium ballistic energy computed with the present configuration* i . e . 14). The energy criterion for stability is the assertion that the given equilibrium state C° characterized by {£°, 0D} is stable against all processes in the c l a s s $(£°, 0°) if and only if the functional T Q h a s , in some s e n s e , a minimum at the configuration F. * To render the energy See, for example, Coleman and Noll [ 2 2 ] , §15.