scholarly journals Scattering Under Linear Non Self-Adjoint Operators: Case of In-Plane Elastic Waves

2021 ◽  
Author(s):  
Amir Ashkan Mokthari ◽  
Yan Lu ◽  
Qiyuan Zhou ◽  
Alireza Vakil Amirkhizi ◽  
Ankit Srivastava
Keyword(s):  
Elastic Waves ◽  
Adjoint Operators

Remarks on nonlinear elastic waves with null conditions

2020 ◽  
Vol 26 ◽  
pp. 121
Author(s):  
Dongbing Zha ◽  
Weimin Peng
Keyword(s):  
Initial Data ◽  
Global Existence ◽  
Elastic Waves ◽  
Wave Equations ◽  
Alternative Proof ◽  
Classical Solutions ◽  
Small Initial Data ◽  
Hyperelastic Materials ◽  
Variational Structure ◽  
Nonlinear Elastic

For the Cauchy problem of nonlinear elastic wave equations for 3D isotropic, homogeneous and hyperelastic materials with null conditions, global existence of classical solutions with small initial data was proved in R. Agemi (Invent. Math. 142 (2000) 225–250) and T. C. Sideris (Ann. Math. 151 (2000) 849–874) independently. In this paper, we will give some remarks and an alternative proof for it. First, we give the explicit variational structure of nonlinear elastic waves. Thus we can identify whether materials satisfy the null condition by checking the stored energy function directly. Furthermore, by some careful analyses on the nonlinear structure, we show that the Helmholtz projection, which is usually considered to be ill-suited for nonlinear analysis, can be in fact used to show the global existence result. We also improve the amount of Sobolev regularity of initial data, which seems optimal in the framework of classical solutions.

Investigating the Excitation of Elastic Waves in an Acoustic Waveguide

Vestnik MEI ◽  
2018 ◽  
Vol 2 (2) ◽  
pp. 129-134
Author(s):  
Andrey A. Kal’shchikov ◽  
Keyword(s):  
Elastic Waves ◽  
Acoustic Waveguide

About features of ultrasonic measurements in coal samples using shear elastic waves

2020 ◽  
Vol 4 ◽  
pp. 117-126
Author(s):  
V.L. Skuratnik ◽  
◽  
P.V. Nikolenko ◽  
P.S. Anufrenkova ◽  
◽  
...  
Keyword(s):  
Elastic Waves ◽  
Ultrasonic Measurements

Dispersion of axisymmetric elastic waves in thick-walled orthotropic pipes

AIAA Journal ◽  
1997 ◽  
Vol 35 ◽  
pp. 1895-1898 ◽  
Author(s):  
Jan Kudlicka
Keyword(s):  
Elastic Waves
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