Control Properties for Second-Order Hyperbolic Systems in Anisotropic Cases with Applications in Inhomogeneous and Anisotropic Elastodynamic Systems

2018 ◽  
Vol 56 (6) ◽  
pp. 4181-4202 ◽  
Author(s):  
Yunxia Shang ◽  
Shumin Li
Keyword(s):  
Hyperbolic Systems ◽  
Second Order

What are second order hyperbolic systems?

1993 ◽  
Vol 44 (2) ◽  
pp. 290-305 ◽  
Author(s):  
Franco Bampi ◽  
Clara Zordan
Keyword(s):  
Hyperbolic Systems ◽  
Second Order

15.—The Propagation of Second-order Lipschitz Discontinuities in Quasi-linear Hyperbolic Systems with Discontinuous Coefficients

1976 ◽  
Vol 74 ◽  
pp. 205-224
Author(s):  
Alan Jeffrey ◽  
Esin Inan
Keyword(s):  
General Theory ◽  
Hyperbolic Systems ◽  
Discontinuous Coefficients ◽  
Second Order ◽  
Strong Discontinuity ◽  
Plane Shear ◽  
Reflected Waves ◽  
Weak Discontinuities ◽  
Derivatives Of ◽  
Transmission And Reflection

SynopsisThis paper develops the general theory of the propagation of Lipschitz discontinuities in first- and second-order partial derivatives of the initial data for a conservative quasi-linear hyperbolic system with discontinuous coefficients. After establishing that such weak discontinuities propagate along characteristics the appropriate transport equations are derived. The effect on this form of wave propagation of the strong discontinuity associatedwith the discontinuous coefficients is then studied and the transmission and reflection characteristics of the resulting waves are analysed. In conclusion, an application of this general theory is made to the propagation of plane shear waves through two different continuous hyperelastic solids to determine the transmitted and reflected waves.

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