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.

scholarly journals Dual-phase-lag one-dimensional thermo-porous-elasticity with microtemperatures

2021 ◽  
Vol 40 (6) ◽  
Author(s):  
Z. Liu ◽  
R. Quintanilla
Keyword(s):  
Heat Conduction ◽  
Elastic Problem ◽  
Linear Operators ◽  
Phase Lag ◽  
Dual Phase ◽  
Polynomial Stability ◽  
One Dimensional ◽  
Semigroups Of Linear Operators ◽  
Relaxation Parameters ◽  
Decay Of Solutions

AbstractThis paper is devoted to studying the linear system of partial differential equations modelling a one-dimensional thermo-porous-elastic problem with microtemperatures in the context of the dual-phase-lag heat conduction. Existence, uniqueness, and exponential decay of solutions are proved. Polynomial stability is also obtained in the case that the relaxation parameters satisfy a certain equality. Our arguments are based on the theory of semigroups of linear operators.

Boundary control of the one-dimensional wave equation

1971 ◽  
Vol 59 (2) ◽  
pp. 291-292
Author(s):  
J.J. Grainger ◽  
D.W. Novotny
Keyword(s):  
Wave Equation ◽  
Boundary Control ◽  
One Dimensional ◽  
The One ◽  
Dimensional Wave
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