Boundary stabilization of wave equations with variable coefficients

2001 ◽  
Vol 44 (3) ◽  
pp. 345-350 ◽  
Author(s):  
Shaoji Feng ◽  
Dexing Feng
Keyword(s):  
Wave Equations ◽  
Variable Coefficients ◽  
Boundary Stabilization

Nonlinear boundary stabilization of the wave equations with variable coefficients and time dependent delay

2014 ◽  
Vol 232 ◽  
pp. 511-520 ◽  
Author(s):  
Zhen-Hu Ning ◽  
Chang-Xiang Shen ◽  
Xiaopeng Zhao ◽  
Hao Li ◽  
Changsong Lin ◽  
...  
Keyword(s):  
Wave Equations ◽  
Nonlinear Boundary ◽  
Variable Coefficients ◽  
Time Dependent ◽  
Boundary Stabilization

Boundary stabilization of compactly coupled wave equations

1997 ◽  
Vol 14 (4) ◽  
pp. 339-359 ◽  
Author(s):  
Vilmos Komornik ◽  
Bopeng Rao
Keyword(s):  
Wave Equations ◽  
Boundary Stabilization ◽  
Coupled Wave Equations ◽  
Coupled Wave

scholarly journals Boundary Stabilization of a Semilinear Wave Equation with Variable Coefficients under the Time-Varying and Nonlinear Feedback

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Bei Gong ◽  
Xiaopeng Zhao
Keyword(s):  
Wave Equation ◽  
Riemannian Geometry ◽  
Nonlinear Term ◽  
Variable Coefficients ◽  
Time Varying ◽  
Nonlinear Feedback ◽  
Boundary Stabilization ◽  
Semilinear Wave Equation ◽  
The Stability ◽  
Stability Results

We study the boundary stabilization of a semilinear wave equation with variable coefficients under the time-varying and nonlinear feedback. By the Riemannian geometry methods, we obtain the stability results of the system under suitable assumptions of the bound of the time-varying term and the nonlinearity of the nonlinear term.

Numerical simulation of higher-order diffusion-wave equations of variable coefficients using the meshless spectral method

2020 ◽  
pp. 2150010
Author(s):  
Manzoor Hussain ◽  
Sirajul Haq
Keyword(s):  
Wave Equations ◽  
Interpolation Method ◽  
Variable Coefficients ◽  
Higher Order ◽  
Implicit Time ◽  
Test Problems ◽  
Time Step ◽  
Diffusion Wave ◽  
Time Step Size ◽  
Time Stepping

In this paper, meshless spectral interpolation technique using implicit time stepping scheme is proposed for the numerical simulations of time-fractional higher-order diffusion wave equations (TFHODWEs) of variable coefficients. Meshless shape functions, obtained from radial basis functions (RBFs) and point interpolation method (PIM), are used for spatial approximation. Central differences coupled with quadrature rule of [Formula: see text] are employed for fractional temporal approximation. For advancement of solution, an implicit time stepping scheme is then invoked. Simulations performed for different benchmark test problems feature good agreement with exact solutions. Stability analysis of the proposed method is theoretically discussed and computationally validated to support the analysis. Accuracy and efficiency of the proposed method are assessed via [Formula: see text], [Formula: see text] and [Formula: see text] error norms as well as number of nodes [Formula: see text] and time step-size [Formula: see text].

Circumferential waves in pre-stressed functionally graded cylindrical curved plates

2014 ◽  
Vol 21 (1) ◽  
pp. 87-97 ◽  
Author(s):  
Jiangong Yu ◽  
Chuanzeng Zhang ◽  
Xiaoming Zhang
Keyword(s):  
Initial Stress ◽  
Wave Equations ◽  
Axial Direction ◽  
Variable Coefficients ◽  
Functionally Graded ◽  
Initial Stresses ◽  
Polynomial Method ◽  
Coupled Wave Equations ◽  
Graded Material ◽  
Polynomial Series

AbstractInitial stress (pre-stress) in functionally graded material (FGM) structures is often inevitable because of the limitation of available manufacturing technology. On the basis of the “mechanics of incremental deformations”, the circumferential wave characteristics in FGM cylindrical curved plates under uniform initial stresses in the radial and axial directions are investigated. The Legendre polynomial series method is used to solve the coupled wave equations with variable coefficients. Through numerical examples, the convergence of the polynomial method is discussed. The influences of the initial stresses on the circumferential Lamb-like and the circumferential SH waves are investigated, respectively. Numerical results show that they are quite distinct. Moreover, the influences of the initial stress in the axial direction are very different from those in the radial direction, both on the dispersion curves and on the displacement and stress distributions.

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