Fractional wave equations with attenuation

被引：13

作者：

Straka, Peter ^{[1
]}

Meerschaert, Mark M. ^{[2
]}

McGough, Robert J. ^{[3
]}

Zhou, Yuzhen ^{[2
]}

机构：

[1] Univ Manchester, Sch Math, Manchester M13 9PL, Lancs, England

[2] Michigan State Univ, Dept Stat & Probabil, E Lansing, MI 48824 USA

[3] Michigan State Univ, Dept Elect & Comp Engn, E Lansing, MI 48824 USA

来源：

FRACTIONAL CALCULUS AND APPLIED ANALYSIS | 2013年 / 16卷 / 01期

关键词：

fractional derivative; wave equation; stable law; continuous time random walk; subordination; attenuation; dispersion; TIME RANDOM-WALKS; MEDIA; DISPERSION; MODELS;

D O I：

10.2478/s13540-013-0016-9

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Fractional 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].

引用

页码：262 / 272

页数：11

共 30 条

[1]

Agrawal O.P., 2000, Fract Calc Appl Anal, V3, P1

[2]

[Anonymous], 1990, PHYS PROPERTIES TISS

[3] Advection and dispersion in time and space [J].

Baeumer, B ;

Benson, DA ;

Meerschaert, MM .

PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS, 2005, 350 (2-4) :245-262

[4] Limit theorem for continuous-time random walks with two time scales [J].

Becker-Kern, P ;

Meerschaert, MM ;

Scheffler, HP .

JOURNAL OF APPLIED PROBABILITY, 2004, 41 (02) :455-466

[5] TRANSIENT SOLUTION FOR SOUND RADIATED INTO A VISCOUS FLUID [J].

BLACKSTOCK, DT .

JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA, 1967, 41 (05) :1312-+

[6] LINEAR MODELS OF DISSIPATION WHOSE Q IS ALMOST FREQUENCY INDEPENDENT-2 [J].

CAPUTO, M .

GEOPHYSICAL JOURNAL OF THE ROYAL ASTRONOMICAL SOCIETY, 1967, 13 (05) :529-&

[7] Fractional Laplacian time-space models for linear and nonlinear lossy media exhibiting arbitrary frequency power-law dependency [J].

Chen, W ;

Holm, S .

JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA, 2004, 115 (04) :1424-1430

[8] Modified Szabo's wave equation models for lossy media obeying frequency power law [J].

Chen, W ;

Holm, S .

JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA, 2003, 114 (05) :2570-2574

[9]

Gorenflo R., 2000, Fract. Calc. Appl. Anal., V3, P75

[10]

Jacob N., 2001, FOURIER ANAL SEMIGRO, VI

← 1 2 3 →