scholarly journals Polynomial stability of the wave equation with distributed delay term on the dynamical control

2021 ◽  
Vol 8 (1) ◽  
pp. 207-227
Author(s):  
Roland Silga ◽  
Gilbert Bayili
Keyword(s):  
Wave Equation ◽  
Frequency Domain ◽  
Distributed Delay ◽  
Strong Stability ◽  
Uniform Stability ◽  
Polynomial Stability ◽  
Delay Term ◽  
Dynamical Control ◽  
Frequency Domain Approach

Abstract Using the frequency domain approach, we prove the rational stability for a wave equation with distributed delay on the dynamical control, after establishing the strong stability and the lack of uniform stability.

scholarly journals Frequency domain approach to decay rates for a coupled hyperbolic-parabolic system

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Bopeng Rao ◽  
Xu Zhang
Keyword(s):  
Asymptotic Behavior ◽  
Wave Equation ◽  
Heat Equation ◽  
Frequency Domain ◽  
Parabolic System ◽  
Decay Rates ◽  
Fluid Structure Interactions ◽  
Fluid Structure ◽  
Structure Interaction ◽  
Frequency Domain Approach

<p style='text-indent:20px;'>We consider the asymptotic behavior of a linear model arising in fluid-structure interactions. The system is formed by a heat equation and a wave equation in two distinct domains, which are coupled by atransmission condition along the interface of the domains. By means of the frequency domain approach, we establish some decay rates for the whole system. Our results also showthat the decay of the fluid-structure interaction depends not only on the transmission of the damping from the heat equation to the wave equation, but also on the location of the damping for the wave equation.</p>

Explicit Stability for a Porous Thermoelastic System with Second Sound and Distributed Delay Term

2021 ◽  
Vol 7 (2) ◽  
Author(s):  
Abdelhak Djebabla ◽  
Abdelbaki Choucha ◽  
Djamel Ouchenane ◽  
Khaled Zennir
Keyword(s):  
Distributed Delay ◽  
Second Sound ◽  
Delay Term

Stabilization of the wave equation with a nonlinear delay term in the boundary conditions

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Wassila Ghecham ◽  
Salah-Eddine Rebiai ◽  
Fatima Zohra Sidiali
Keyword(s):  
Wave Equation ◽  
Original Problem ◽  
Existence Of Solutions ◽  
Semigroup Theory ◽  
Decay Rates ◽  
Uniform Decay ◽  
Delay Term ◽  
Nonlinear Semigroup Theory ◽  
Nonlinear Boundary Feedback ◽  
Nonlinear Delay

Abstract A wave equation in a bounded and smooth domain of ℝ n {\mathbb{R}^{n}} with a delay term in the nonlinear boundary feedback is considered. Under suitable assumptions, global existence and uniform decay rates for the solutions are established. The proof of existence of solutions relies on a construction of suitable approximating problems for which the existence of the unique solution will be established using nonlinear semigroup theory and then passage to the limit gives the existence of solutions to the original problem. The uniform decay rates for the solutions are obtained by proving certain integral inequalities for the energy function and by establishing a comparison theorem which relates the asymptotic behavior of the energy and of the solutions to an appropriate dissipative ordinary differential equation.

scholarly journals A frequency‐domain approach for damage detection in welded structures

2021 ◽  
Author(s):  
Camilla Ronchei ◽  
Sabrina Vantadori ◽  
Andrea Carpinteri ◽  
Ignacio Iturrioz ◽  
Roberto Issopo Rodrigues ◽  
...  
Keyword(s):  
Damage Detection ◽  
Frequency Domain ◽  
Welded Structures ◽  
Frequency Domain Approach
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