Well-posedness and stability for a viscoelastic wave equation with density and time-varying delay in $\mathbb {R}^n$

2019 ◽  
Vol 31 (4) ◽  
pp. 465-493
Author(s):  
Baowei Feng ◽  
Xinguang Yang ◽  
Keqin Su
Keyword(s):  
Wave Equation ◽  
Well Posedness ◽  
Time Varying ◽  
Time Varying Delay ◽  
Viscoelastic Wave Equation ◽  
Viscoelastic Wave ◽  
Varying Delay

scholarly journals Uniform decay for a viscoelastic wave equation with density and time-varying delay in Rn

Filomat ◽  
2019 ◽  
Vol 33 (3) ◽  
pp. 961-970
Author(s):  
Salah Zitouni ◽  
Khaled Zennir ◽  
Lamine Bouzettouta
Keyword(s):  
Wave Equation ◽  
Relaxation Function ◽  
Time Varying ◽  
Delay Term ◽  
Time Varying Delay ◽  
Viscoelastic Wave Equation ◽  
Viscoelastic Wave ◽  
Linear Viscoelastic ◽  
Energy Perturbation ◽  
Varying Delay

A linear viscoelastic wave equation with density and a time-varying delay term in the internal feedback is considered. Under suitable assumptions on the relaxation function, we establish a decay result of solution for by using energy perturbation method in the space Rn (n > 2). We extend a recent result in Feng [10].

scholarly journals Well-Posedness and Stability Result of the Nonlinear Thermodiffusion Full von Kármán Beam with Thermal Effect and Time-Varying Delay

2021 ◽  
Vol 2021 ◽  
pp. 1-16
Author(s):  
Abdelbaki Choucha ◽  
Djamel Ouchenane ◽  
Salah Mahmoud Boulaaras ◽  
Bahri Belkacem Cherif ◽  
Mohamed Abdalla
Keyword(s):  
Stability Result ◽  
Beam Model ◽  
Well Posedness ◽  
Time Varying ◽  
Heat And Mass Exchange ◽  
Time Varying Delay ◽  
Von Karman ◽  
Diffusion Effects ◽  
Von Kármán ◽  
Varying Delay

In this work, we consider a new full von Kármán beam model with thermal and mass diffusion effects according to the Gurtin-Pinkin model combined with time-varying delay. Heat and mass exchange with the environment during thermodiffusion in the von Kármán beam. We establish the well-posedness and the exponential stability of the system by the energy method under suitable conditions.

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