scholarly journals Global Weak Solutions to a Generalized Hyperelastic-rod Wave Equation

2005 ◽  
Vol 37 (4) ◽  
pp. 1044-1069 ◽  
Author(s):  
G. M. Coclite ◽  
H. Holden ◽  
K. H. Karlsen
Keyword(s):  
Wave Equation ◽  
Weak Solutions ◽  
Global Weak Solutions

scholarly journals On the Existence of Global Weak Solutions for a Weakly Dissipative Hyperelastic Rod Wave Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Haibo Yan ◽  
Ls Yong ◽  
Yu Yang ◽  
Yang Wang
Keyword(s):  
Wave Equation ◽  
Weak Solutions ◽  
Global Weak Solutions ◽  
Initial Value

Assuming that the initial valuev0(x)belongs to the spaceH1(R), we prove the existence of global weak solutions for a weakly dissipative hyperelastic rod wave equation in the spaceC([0,∞)×R)⋂‍L∞([0,∞);H1(R)). The limit of the viscous approximation for the equation is used to establish the existence.

scholarly journals Fractional wave equations with attenuation

2013 ◽  
Vol 16 (1) ◽  
Author(s):  
Peter Straka ◽  
Mark Meerschaert ◽  
Robert McGough ◽  
Yuzhen Zhou
Keyword(s):  
Wave Equation ◽  
Power Law ◽  
Weak Solutions ◽  
Wave Equations ◽  
Inhomogeneous Media ◽  
Medical Ultrasound ◽  
Sound Waves ◽  
Fractional Wave Equations

AbstractFractional wave equations with attenuation have been proposed by Caputo [5], Szabo [28], Chen and Holm [7], and Kelly et al. [11]. These equations capture the power-law attenuation with frequency observed in many experimental settings when sound waves travel through inhomogeneous media. In particular, these models are useful for medical ultrasound. This paper develops stochastic solutions and weak solutions to the power law wave equation of Kelly et al. [11].

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