PublicaciĂłn: GEVREY CLASS OF LOCALLY DISSIPATIVE EULER-BERNOULLI BEAM EQUATION
Fecha
2021
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SIAM JOURNAL ON CONTROL AND OPTIMIZATION
Resumen
WE STUDY THE SEMIGROUP ASSOCIATED TO THE EULER--BERNOULLI BEAM EQUATION WITH LOCALIZED (DISCONTINUOUS) DISSIPATION. WE ASSUME THAT THE BEAM IS COMPOSED OF THREE COMPONENTS: ELASTIC, VISCOELASTIC OF KELVIN--VOIGT TYPE, AND THERMOELASTIC PARTS. WE PROVE THAT THIS MODEL GENERATES A SEMIGROUP OF GEVREY CLASS THAT IN PARTICULAR IMPLIES THE EXPONENTIAL STABILITY OF THE MODEL. TO OUR KNOWLEDGE, THIS IS THE FIRST POSITIVE RESULT GIVING INCREASED REGULARITY FOR THE EULER--BERNOULLI BEAM WITH LOCALIZED DAMPING.
