scholarly journals General decay for a wave equation of Kirchhoff type with a boundary control of memory type

2011 ◽  
Vol 2011 (1) ◽  
Author(s):  
Shun-Tang Wu
Keyword(s):  
Wave Equation ◽  
Boundary Control ◽  
General Decay ◽  
Kirchhoff Type ◽  
Memory Type

A general decay result of a wave equation with a dynamic boundary control of diffusive type

2019 ◽  
Vol 42 (8) ◽  
pp. 2721-2733
Author(s):  
Farida Cheheb ◽  
Hanane Benkhedda ◽  
Abbes Benaissa
Keyword(s):  
Wave Equation ◽  
Boundary Control ◽  
General Decay ◽  
Dynamic Boundary

scholarly journals A New General Decay Rate of Wave Equation with Memory-Type Boundary Control

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Sheng Fan
Keyword(s):  
Wave Equation ◽  
Decay Rate ◽  
General Decay ◽  
Forced Oscillations ◽  
Memory Term ◽  
General Decay Rate ◽  
Damped Oscillations ◽  
Memory Type ◽  
Type Boundary ◽  
With Memory

Of interest is a wave equation with memory-type boundary oscillations, in which the forced oscillations of the rod is given by a memory term at the boundary. We establish a new general decay rate to the system. And it possesses the character of damped oscillations and tends to a finite value for a large time. By assuming the resolvent kernel that is more general than those in previous papers, we establish a more general energy decay result. Hence the result improves earlier results in the literature.

scholarly journals General decay and blow up of solutions for a variable-exponent viscoelastic double-Kirchhoff type wave equation with nonlocal degenerate damping

2021 ◽  
Author(s):  
Mohammad Shahrouzi ◽  
Jorge Ferreira ◽  
Erhan Pişkin
Keyword(s):  
Wave Equation ◽  
Variable Exponent ◽  
Blow Up ◽  
Type Equation ◽  
Initial Energy ◽  
General Decay ◽  
Kirchhoff Type ◽  
Type Wave ◽  
Positive Initial Energy ◽  
Viscoelastic Term

In this paper we consider a viscoelastic double-Kirchhoff type wave equation of the form $$ u_{tt}-M_{1}(\|\nabla u\|^{2})\Delta u-M_{2}(\|\nabla u\|_{p(x)})\Delta_{p(x)}u+(g\ast\Delta u)(x,t)+\sigma(\|\nabla u\|^{2})h(u_{t})=\phi(u), $$ where the functions $M_{1},M_{2}$ and $\sigma, \phi$ are real valued functions and $(g\ast\nabla u)(x,t)$ is the viscoelastic term which are introduced later. Under appropriate conditions for the data and exponents, the general decay result and blow-up of solutions are proved with positive initial energy. This study extends and improves the previous results in the literature to viscoelastic double-Kirchhoff type equation with degenerate nonlocal damping and variable-exponent nonlinearities.

scholarly journals Asymptotic behavior for a viscoelastic Kirchhoff equation with distributed delay and Balakrishnan–Taylor damping

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Abdelbaki Choucha ◽  
Salah Boulaaras
Keyword(s):  
Asymptotic Behavior ◽  
Decay Rate ◽  
Energy Method ◽  
Distributed Delay ◽  
Type Equation ◽  
General Decay ◽  
Kirchhoff Equation ◽  
General Decay Rate ◽  
Kirchhoff Type ◽  
Nonlinear Viscoelastic

AbstractA nonlinear viscoelastic Kirchhoff-type equation with Balakrishnan–Taylor damping and distributed delay is studied. By the energy method we establish the general decay rate under suitable hypothesis.

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