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Un résultat sur les fonctions de classe C 1 , α et application au problème de Cauchy

Robert Dalmasso (1986)

Annales de l'institut Fourier

Nous montrons principalement que, si f 0 est une fonction différentiable sur un intervalle [ 0 , T ] , si sa dérivée est höldérienne d’ordre α avec 0 < α 1 et si f ' ( 0 ) = 0 (resp. f ' ( T ) = 0 ) quand f ( 0 ) = 0 (resp. f ( T ) = 0 ) alors f 1 / ( 1 + α ) , qui est absolument continue, admet (presque partout) une dérivée bornée presque partout.

Uniform controllability for the beam equation with vanishing structural damping

Ioan Florin Bugariu (2014)

Czechoslovak Mathematical Journal

This paper is devoted to studying the effects of a vanishing structural damping on the controllability properties of the one dimensional linear beam equation. The vanishing term depends on a small parameter ε ( 0 , 1 ) . We study the boundary controllability properties of this perturbed equation and the behavior of its boundary controls v ε as ε goes to zero. It is shown that for any time T sufficiently large but independent of ε and for each initial data in a suitable space there exists a uniformly bounded...

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