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UID:5169@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20240528T110000
DTEND;TZID=Europe/Paris:20240528T120000
DTSTAMP:20240528T093456Z
URL:https://www.i2m.univ-amu.fr/evenements/tba-107/
SUMMARY: (...): Regularity of the semigroup associated with some interactin
 g elastic systems
DESCRIPTION:: In this talk\, we examine regularity and stability issues for
  two damped abstract elastic systems. The damping involves the average vel
 ocity and a fractional power $theta$\, with $theta$ in $[-1\, 1]$\, of the
  principal operator. The matrix operator defining the damping mechanism fo
 r the coupled system is degenerate. First\, we prove that for $theta$ in $
 (frac{1}{2}\,1]$\, the underlying semigroup is not analytic\, but is diffe
 rentiable for $theta$ in $(0\, 1)$\; this is in sharp contrast with known 
 results for a singlesimilarly damped elastic system\, where the semigroup 
 is analytic for $theta$ in $[frac{1}{2}\, 1]$\; this shows that the degene
 racy dominates the dynamics of the interacting systems\, preventing analyt
 icity in that range. Next\, we show that\nfor $theta$ in $(0\, frac{1}{2}]
 $\, the semigroup is of certain Gevrey classes. Finally\, we show that the
  semigroup decays exponentially for $theta$ in $[0\, 1]$\, and polynomiall
 y for $theta$ in $[-1\, 0)$. To prove our results\, we use the frequency d
 omain method\, which relies on resolvent estimates. Optimality of our reso
 lvent estimates is also established. Two examples of application are provi
 ded.
CATEGORIES:Séminaire,Analyse Appliquée
LOCATION:I2M Saint-Charles - Salle de séminaire\, Université Aix-Marseill
 e\, Campus Saint-Charles\, 3 Place Victor Hugo\, Marseille\, 13003\, Franc
 e
X-APPLE-STRUCTURED-LOCATION;VALUE=URI;X-ADDRESS=Université Aix-Marseille\,
  Campus Saint-Charles\, 3 Place Victor Hugo\, Marseille\, 13003\, France;X
 -APPLE-RADIUS=100;X-TITLE=I2M Saint-Charles - Salle de séminaire:geo:0,0
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