Wave propagation in media with singular memory

Mathematical and Computer Modelling

Volumn 34, Issue 12-13, 2001, Pages 1399-1421

  Hanyga, A ^a  

^a UNIVERSITY OF BERGEN   (Norway)

Author keywords

Integrodifferential equation; Poroelasticity; Viscoelasticity

Indexed keywords

EID: 0035813991     PISSN: 08957177     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0895-7177(01)00137-6     Document Type: Article

References (95)

1. Zur dispersionstheorie des schalles
2. Thermodynamics with internal state variables
3. Zur theorie der elastischen nachwirkung
4. Deformation in relation to time, pressure and temperature
5. On fractional differentials
6. The rheological law underlying the Nutting equation
7. Applications of fractional calculus to the theory of viscoelasticity
8. Polynomial operators, Stieltjes convolution, and fractional calculus in hereditary mechanics
9. Time domain wave equations for lossy media obeying a frequency power law
10. Causal theories and data for acoustic attenuation obeying a frequency power law
11. Representation of absorption of non-linear waves by fractional derivatives
12. Wave propagation in micro-heterogeneous porous media: A model based on an integrodifferential equation
13. Laws of mechanical relaxation processes in polymers
14. Mechanical stress relaxation in polymers: Fractional integral order vs. fractional differential order
15. Rheological material functions for associating comb-shaped or H-shaped polymers: A fractional calculus approach
16. Linear viscoelastic behavior of branched polybutadiene: A fractional calculus approach
17. Linear viscoelastic behavior of complex polymeric materials: A fractional model representation
18. On the applications of fractional calculus for the formulation of viscoelastic models
19. A fractional model for mechanical stress relaxation
20. Fractional integral operators and Fox functions in the theory of viscoelasticity
21. Fractional relaxation and the time-temperature superposition principle
22. A kinetic theory for polymer melts, I. The equation for the single-link oricntational distribution function
23. On the truncation of the infinite sum of exponentials in a memory kernel of the linear wave equation
24. Fractional diffusion equation and relaxation in complex viscoelastic materials
25. Nonlinear acoustics (theoretical)
26. Time domain solution of Kirchhoff's equation for sound propagation in viscothermal gases: A diffusion process
27. Acoustical characteristics of rigid fibrous absorbents and granular materials
28. A theoretical basis for the application of fractional calculus to viscoelaticity
29. Dispersion and absorption in dielectrics, I: Alternating current characteristics
30. Asymptotic expansions for transient viscoelastic waves
31. Some remarks on the propagation and non-propagation of discontinuities in linearly viscoelastic liquids
32. On wave propagation in linear viscoelasticity
33. A model equation for viscoelasticity with a strongly singular kernel
34. Asymptotic behaviour of viscoelastic waves
35. Viscoelastic pulse propagation and stable probability distributions
36. The propagation of stress pulses in viscoelastic solids
37. Theory of acoustic attenuation, dispersion and pulse propagation in unconsolidated granulated materials including marine sediments
38. Theory of compressional and shear waves in fluidlike marine sediments
39. Asymptotic wavefront expansions in hereditary media with singular memory kernels
40. Asymptotic ray theory in poro- and viscoelastic media
41. Spectral and time-domain consequences of an integro-differential equation perturbation of the wave equation
42. Fundamental solutions of the wave equation with delayed time
43. Automodel solutions of wave equations with time lag
44. Some effects of the memory kernel singularity on wave propagation and inversion in poroelastic media, I: Forward modeling
45. Transformation de laplace des distributions
46. Fractional calculus: Some basic problems
47. Simple memory models of attenuation in complex viscoporous media
48. Smoothing properties of linear Volterra integrodifferential equations
49. Singular relaxation moduli and smoothing in three-dimensional viscoelasticity
50. The propagation of plane sound waves in narrow and wide circular tubes, and generalization to uniform tubes of arbitrary cross-section
51. Propagation of sound and the assignment of shape factors in model porous materials having simple pore geometries
52. On acoustical models for sound propagation in rigid frame porous materials and the influence of shape factors
53. New empirical equations for sound propagation in rigid frame fibrous materials
54. Relaxation-matched modelling of propagation through porous media, including fractal pore structure
55. Simple, relaxational models for the acoustical properties of porous media
56. On the fractional calculus model of viscoelastic behavior
57. Discretized fractional calculus
58. Convolution quadrature and discretized fractional calculus, I-II
59. Numerical solutions of a poro-acoustic wave equation with generalized fractional integral operators
60. Completely positive measures and Feller semigroups
61. Cosine operator functions
62. Una caratterizzazione del generatori di funzioni coseno astratte
63. Cosine families of operators and applications