Energy Decay of Solutions to a Wave Equation with a Dynamic Boundary Dissipation of Fractional Derivative Type

2018 ◽  
Vol 37 (3) ◽  
pp. 315-339 ◽  
Author(s):  
Abbes Benaissa ◽  
Hanane Benkhedda
Keyword(s):  
Wave Equation ◽  
Fractional Derivative ◽  
Energy Decay ◽  
Dynamic Boundary ◽  
Decay Of Solutions ◽  
Derivative Type ◽  
Boundary Dissipation

scholarly journals Energy decay for a degeneratewave equation under fractional derivative controls

Filomat ◽  
2018 ◽  
Vol 32 (17) ◽  
pp. 6045-6072
Author(s):  
Abbes Benaissa ◽  
Chahira Aichi
Keyword(s):  
Wave Equation ◽  
Fractional Derivative ◽  
Boundary Control ◽  
Semigroup Theory ◽  
Energy Decay ◽  
Linear Operators ◽  
Polynomial Stability ◽  
One Dimensional ◽  
Spectrum Method ◽  
Derivative Type

In this article, we consider a one-dimensional degenerate wave equation with a boundary control condition of fractional derivative type. We show that the problem is not uniformly stable by a spectrum method and we study the polynomial stability using the semigroup theory of linear operators.

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