Second Darboux problem for the wave equation with a power-law nonlinearity

2013 ◽  
Vol 49 (12) ◽  
pp. 1577-1595 ◽  
Author(s):  
S. S. Kharibegashvili ◽  
O. M. Dzhokhadze
Keyword(s):  
Wave Equation ◽  
Power Law ◽  
Darboux Problem

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].

A continuous power law wave equation for biomedical ultrasound

2018 ◽  
Vol 143 (3) ◽  
pp. 1802-1802
Author(s):  
James F. Kelly ◽  
Mark M. Meerschaert ◽  
Robert McGough
Keyword(s):  
Wave Equation ◽  
Power Law ◽  
Continuous Power

scholarly journals The mechanism of fractured sandstone in compaction creep process

2019 ◽  
Vol 23 (Suppl. 3) ◽  
pp. 989-995
Author(s):  
Zhanguo Ma ◽  
Minchao Zhang ◽  
Shixing Cheng ◽  
Jun Hu ◽  
Yang Su ◽  
...  
Keyword(s):  
Wave Equation ◽  
Analytical Solution ◽  
Fractional Order ◽  
Power Law ◽  
Creep Process ◽  
Order Model ◽  
Fractional Order Model ◽  
Complex Power ◽  
Fractured Sandstone ◽  
Derivatives Of

In this paper, we consider the general fractional-order derivatives of the Liouville-Sonine-Caputo and Liouville-Sonine type containing the Lorenzo-Hartley kernel. A general fractional-order model for the wave equation with the analytical solution is discussed in detail. The general fractional-order formula is accurate and efficient for description of the complex, power-law and memory behaviors for the mining rock.

scholarly journals On a fractional Zener elastic wave equation

2013 ◽  
Vol 16 (1) ◽  
Author(s):  
Sven Näsholm ◽  
Sverre Holm
Keyword(s):  
Wave Equation ◽  
Elastic Wave ◽  
Power Law ◽  
Continuous Distribution ◽  
Special Focus ◽  
Elastic Wave Equation ◽  
Stress Strain ◽  
Strain Relation ◽  
Stress Strain Relation ◽  
Viscoelastic Element

AbstractThis survey concerns a causal elastic wave equation which implies frequency power-law attenuation. The wave equation can be derived from a fractional Zener stress-strain relation plus linearized conservation of mass and momentum. A connection between this four-parameter fractional wave equation and a physically well established multiple relaxation acoustical wave equation is reviewed. The fractional Zener wave equation implies three distinct attenuation power-law regimes and a continuous distribution of compressibility contributions which also has power-law regimes. Furthermore it is underlined that these wave equation considerations are tightly connected to the representation of the fractional Zener stress-strain relation, which includes the spring-pot viscoelastic element, and by a Maxwell-Wiechert model of conventional springs and dashpots. A purpose of the paper is to make available recently published results on fractional calculus modeling in the field of acoustics and elastography, with special focus on medical applications.

A variational method for determining eigenvalues of the wave equation applied to tropospheric refraction

1947 ◽  
Vol 43 (2) ◽  
pp. 213-219 ◽  
Author(s):  
G. G. MacFarlane
Keyword(s):  
Refractive Index ◽  
Wave Equation ◽  
Variational Method ◽  
Power Law ◽  
Complex Eigenvalues ◽  
Tropospheric Refraction ◽  
Direct Variational Method ◽  
Anomalous Propagation ◽  
Better Than

A simple and direct variational method is described for finding both complex and real eigenvalues of the wave equation of anomalous propagation in a horizontally stratified atmosphere. It may be looked upon as an extension of Rayleigh's method to complex eigenvalues. In this paper it is illustrated by an example, taken from the duct theory of super-refraction, in which the refractive index of the air varies with height according to a power law. Numerical agreement in the values for the lowest order eigenvalues with those obtained by the differential analyser is better than ½%.

scholarly journals An analytical solution for solving a new general fractional-order model for wave in mining rock

2019 ◽  
Vol 23 (Suppl. 3) ◽  
pp. 983-987
Author(s):  
Anye Cao ◽  
Xiao-Jun Yang ◽  
Yiying Feng
Keyword(s):  
Wave Equation ◽  
Analytical Solution ◽  
Fractional Order ◽  
Power Law ◽  
Order Model ◽  
Fractional Order Model ◽  
Complex Power ◽  
Derivatives Of

In this paper, we consider the general fractional-order derivatives of the Liouville-Sonine-Caputo and Liouville-Sonine type containing the Lorenzo-Hartley kernel. A general fractional-order model for the wave equation with the analytical solution is discussed in detail. The general fractional-order formula is accurate and efficient for description of the complex, power-law and memory behaviors for the mining rock.

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