theory of wave propagation; fronts; rays; effective models.
Main publications:
G. I. Petrashen, L. A. Molotkov, P. V. Krauklis. Volny v sloisto-odnorodnykh izotropnykh uprugikh sredakh. L.: Nauka, t. 1, 1982, 289 s.; t. 2, 1986, 304 s.
L. A. Molotkov. Matrichnyi metod v teorii rasprostraneniya voln v sloistykh uprugikh i zhidkikh sredakh. L.: Nauka, 1984, 201 s.
A. V. Bakulin. Effektivnye seismicheskie modeli treschinovatykh i poristykh sred. SPb: Izd-vo SPb un-ta, 1998, 141 s.
L. A. Molotkov Issledovanie rasprostraneniya voln v poristykh i treschinovatykh sredakh na osnove effektivnykh modelei Bio i sloistykh sred. SPb: Nauka, 2001, 348 s.
L. A. Molotkov, “Propagation of normal waves in porous rod with opened pores on boundaries”, Zap. Nauchn. Sem. POMI, 393 (2011), 211–223; J. Math. Sci. (N. Y.), 185:4 (2012), 630–637
L. A. Molotkov, “Propagation of normal waves in porous rod with closed pores on boundaries”, Zap. Nauchn. Sem. POMI, 393 (2011), 191–210; J. Math. Sci. (N. Y.), 185:4 (2012), 619–629
L. A. Molotkov, “Normal waves in porous layer with opened pores on one boundary and with closed pores on other boundary”, Zap. Nauchn. Sem. POMI, 393 (2011), 178–190; J. Math. Sci. (N. Y.), 185:4 (2012), 611–618
L. A. Molotkov, “About the Rayleigh wave on curvilinear boundary between elastic and fluid media”, Zap. Nauchn. Sem. POMI, 380 (2010), 90–109; J. Math. Sci. (N. Y.), 175:6 (2011), 672–684
L. A. Molotkov, “About the slow waves in curvilinear fluid layers”, Zap. Nauchn. Sem. POMI, 379 (2010), 67–87; J. Math. Sci. (N. Y.), 173:3 (2011), 278–290
2009
6.
L. A. Molotkov, A. A. Mukhin, “Investigation of normal waves in a porous layer surrounded by elastic half-spaces”, Zap. Nauchn. Sem. POMI, 369 (2009), 127–142; J. Math. Sci. (N. Y.), 167:5 (2010), 670–679
L. A. Molotkov, “Investigation of low frequency normal waves in Biot layer surrounded by an elastic medium”, Zap. Nauchn. Sem. POMI, 369 (2009), 110–126; J. Math. Sci. (N. Y.), 167:5 (2010), 660–669
A. P. Krauklis, P. V. Krauklis, L. A. Molotkov, “To the problem of while production hydrocarbon reservoir monitoring”, Zap. Nauchn. Sem. POMI, 369 (2009), 64–94; J. Math. Sci. (N. Y.), 167:5 (2010), 632–650
9.
N. Ya. Kirpichnikova, L. A. Molotkov, “On the velocity of the Rayleigh wave propagating along curvilinear surfaces”, Zap. Nauchn. Sem. POMI, 369 (2009), 48–63; J. Math. Sci. (N. Y.), 167:5 (2010), 622–631
L. A. Molotkov, “Wave propagation in an isolated porous Biot layer with closed pores on the boundaries”, Zap. Nauchn. Sem. POMI, 354 (2008), 173–189; J. Math. Sci. (N. Y.), 155:3 (2008), 432–441
L. A. Molotkov, “Investigation of front tangency of two transversal waves in transverse isotropic elastic media”, Zap. Nauchn. Sem. POMI, 342 (2007), 206–216; J. Math. Sci. (N. Y.), 148:5 (2008), 753–759
L. A. Molotkov, “Investigation of wave field in effective model of layered elastic medium with slide contact on interfaces”, Zap. Nauchn. Sem. POMI, 342 (2007), 187–205; J. Math. Sci. (N. Y.), 148:5 (2008), 741–725
2006
14.
L. A. Molotkov, M. N. Perekareva, “Investigation of wave field in effective model of layered elastic-fluid medium”, Zap. Nauchn. Sem. POMI, 332 (2006), 175–192; J. Math. Sci. (N. Y.), 142:6 (2007), 2620–2629
L. A. Molotkov, “On one asymmetric wave field in transversely isotropic elastic medium”, Zap. Nauchn. Sem. POMI, 332 (2006), 163–174; J. Math. Sci. (N. Y.), 142:6 (2007), 2613–2619
L. A. Molotkov, “Investigation of wave propagation velocities in fluid mixtures”, Zap. Nauchn. Sem. POMI, 332 (2006), 149–162; J. Math. Sci. (N. Y.), 142:6 (2007), 2605–2612
17.
P. V. Krauklis, L. A. Molotkov, A. P. Krauklis, “Tube wave from a point source, placed outside the borehole”, Zap. Nauchn. Sem. POMI, 332 (2006), 99–122; J. Math. Sci. (N. Y.), 142:6 (2007), 2376–2588
L. A. Molotkov, “Estimating inequalities for velocities of propagation and for effective densities in fluid mixtures”, Zap. Nauchn. Sem. POMI, 324 (2005), 180–189; J. Math. Sci. (N. Y.), 138:2 (2006), 5584–5589
19.
L. A. Molotkov, “On attenuation of waves propagating in fluid mixtures”, Zap. Nauchn. Sem. POMI, 324 (2005), 148–179; J. Math. Sci. (N. Y.), 138:2 (2006), 5565–5583
2004
20.
L. A. Molotkov, “About propagation of seismic waves in block elastic-fluid media. III”, Zap. Nauchn. Sem. POMI, 308 (2004), 147–160; J. Math. Sci. (N. Y.), 132:1 (2006), 83–90
L. A. Molotkov, “About propagation of seismic waves in block fluid media”, Zap. Nauchn. Sem. POMI, 308 (2004), 124–146; J. Math. Sci. (N. Y.), 132:1 (2006), 69–82
L. A. Molotkov, “About propagation of seismic waves in block elastic-fluid media. II”, Zap. Nauchn. Sem. POMI, 297 (2003), 254–271; J. Math. Sci. (N. Y.), 127:6 (2005), 2482–2491
L. A. Molotkov, “About propagation of seismic waves in block elastic-fluid media. I”, Zap. Nauchn. Sem. POMI, 297 (2003), 230–253; J. Math. Sci. (N. Y.), 127:6 (2005), 2469–2481
L. A. Molotkov, “On the wave attenuation in the effective model describing porous and fractured media saturated by fluid”, Zap. Nauchn. Sem. POMI, 297 (2003), 216–229; J. Math. Sci. (N. Y.), 127:6 (2005), 2461–2468
L. A. Molotkov, “On wave propagation in the elastic medium intersected by systems of parallel fractures”, Zap. Nauchn. Sem. POMI, 285 (2002), 165–193; J. Math. Sci. (N. Y.), 122:5 (2004), 3548–3563
L. A. Molotkov, “On one effictive model of a fractured medium”, Zap. Nauchn. Sem. POMI, 285 (2002), 150–164; J. Math. Sci. (N. Y.), 122:5 (2004), 3539–3547
2001
27.
L. A. Molotkov, “The effective model of the layered medium in which porous and elastic layers being in slide contact alternate”, Zap. Nauchn. Sem. POMI, 275 (2001), 165–186; J. Math. Sci. (N. Y.), 117:2 (2003), 3982–3993
L. A. Molotkov, “The effective model of porous block medium with slide contact on interfaces”, Zap. Nauchn. Sem. POMI, 275 (2001), 140–164; J. Math. Sci. (N. Y.), 117:2 (2003), 3968–3981
L. A. Molotkov, “On a inner source in transversely isotropic elastic medium”, Zap. Nauchn. Sem. POMI, 264 (2000), 238–249; J. Math. Sci. (New York), 111:5 (2002), 3763–3769
L. A. Molotkov, “About the sources acting on the free boundary of porous Biot medium and about reflection on this boundary”, Zap. Nauchn. Sem. POMI, 264 (2000), 217–237; J. Math. Sci. (New York), 111:5 (2002), 3750–3762
L. A. Molotkov, “About the matrix method in the theory of wave propagation in layered porous Biot media”, Zap. Nauchn. Sem. POMI, 264 (2000), 197–216; J. Math. Sci. (New York), 111:5 (2002), 3737–3749
1999
32.
L. A. Molotkov, “On the effective model of porous stratified media with slide contact between layers”, Zap. Nauchn. Sem. POMI, 257 (1999), 184–206; J. Math. Sci. (New York), 108:5 (2002), 772–789
L. A. Molotkov, “On propagation of normal waves in an isolated porous saturated by fluid Biot layer”, Zap. Nauchn. Sem. POMI, 257 (1999), 165–183; J. Math. Sci. (New York), 108:5 (2002), 758–771
L. A. Molotkov, “On coefficients of pore tortuosity in the effective Biot model”, Zap. Nauchn. Sem. POMI, 257 (1999), 157–164; J. Math. Sci. (New York), 108:5 (2002), 752–757
L. A. Molotkov, A. V. Bakulin, “On attenuation in layered porous Biot media and their effective models”, Zap. Nauchn. Sem. POMI, 250 (1998), 244–262; J. Math. Sci. (New York), 102:4 (2000), 4291–4303
36.
L. A. Molotkov, “On the derivation methods of the equations describing the effective models of layered media”, Zap. Nauchn. Sem. POMI, 250 (1998), 219–243; J. Math. Sci. (New York), 102:4 (2000), 4275–4290
L. A. Molotkov, A. V. Bakulin, “The jumps of displacements and stresses as seismic sources in Biot medium”, Zap. Nauchn. Sem. POMI, 239 (1997), 164–196; J. Math. Sci. (New York), 96:4 (1999), 3386–3406
38.
L. A. Molotkov, A. V. Bakulin, “The effective models of the stratified media containing porous Biot layers”, Zap. Nauchn. Sem. POMI, 239 (1997), 140–163; J. Math. Sci. (New York), 96:4 (1999), 3371–3385
L. A. Molotkov, A. V. Bakulin, “Sources of the center of dilatation and center of compression types in the Biot model”, Zap. Nauchn. Sem. POMI, 230 (1995), 196–213; J. Math. Sci. (New York), 91:2 (1998), 2828–2839
L. A. Molotkov, A. V. Bakulin, “The effective model of a stratified solid-fluid medium as a special case of the Biot model”, Zap. Nauchn. Sem. POMI, 230 (1995), 172–195; J. Math. Sci. (New York), 91:2 (1998), 2812–2827
L. A. Molotkov, A. V. Bakulin, “Effective model of the fractured medium with fractures characterized as displacements discontinuity surfaces”, Zap. Nauchn. Sem. POMI, 218 (1994), 118–137; J. Math. Sci. (New York), 86:3 (1997), 2735–2746
L. A. Molotkov, “On the effective model of elastic block medium with slide contact on interfaces”, Zap. Nauchn. Sem. POMI, 218 (1994), 96–117; J. Math. Sci. (New York), 86:3 (1997), 2721–2734
L. A. Molotkov, “On the efffective model, describing a layered periodic elastic medium with slide contacts on interfaces”, Zap. Nauchn. Sem. POMI, 210 (1994), 192–212; J. Math. Sci., 83:2 (1997), 288–301
L. A. Molotkov, “The equations of the efffective model of anisotropic elastic medium with cracks filled with liquid”, Zap. Nauchn. Sem. POMI, 210 (1994), 175–191; J. Math. Sci., 83:2 (1997), 278–287
1992
45.
L. A. Molotkov, “On the twophase effective model of the medium with cracks of a finite length”, Zap. Nauchn. Sem. POMI, 203 (1992), 137–155; J. Math. Sci., 79:4 (1996), 1247–1259
1991
46.
L. A. Molotcov, “On the new approach of obtaining of average effective model equations of periodic media”, Zap. Nauchn. Sem. LOMI, 195 (1991), 82–102; J. Soviet Math., 62:6 (1992), 3103–3117
L. A. Molotkov, “The equations of effective twophase crack model with cracks of a finite length”, Zap. Nauchn. Sem. LOMI, 186 (1990), 142–153; J. Math. Sci., 73:3 (1995), 389–396
1989
48.
L. A. Molotkov, “On the investigation of wave propagation in the models of cracked media”, Zap. Nauchn. Sem. LOMI, 179 (1989), 116–127; J. Soviet Math., 57:3 (1991), 3140–3146
1988
49.
L. A. Molotkov, “Wave propagation particularities in the layered models of cracked media”, Zap. Nauchn. Sem. LOMI, 173 (1988), 123–133; J. Soviet Math., 55:3 (1991), 1732–1740
L. A. Molotkov, “Vibration equations of plates with general anisotropy”, Zap. Nauchn. Sem. LOMI, 165 (1987), 122–135
1986
51.
L. A. Molotkov, A. E. Khilo, “The effective models of layered elastic media with linear contacts of general type”, Zap. Nauchn. Sem. LOMI, 156 (1986), 148–157
52.
L. A. Molotkov, P. V. Krauklis, “A note about experimental determination of Poisson's ratio in the cracked media”, Zap. Nauchn. Sem. LOMI, 156 (1986), 143–147
1984
53.
L. A. Molotkov, A. E. Khilo, “Averaging periodic, nonideal elastic media”, Zap. Nauchn. Sem. LOMI, 140 (1984), 123–131; J. Soviet Math., 32:2 (1986), 186–192
L. A. Molotkov, A. E. Khilo, “Single-phase and multiphase effective models describing periodic media”, Zap. Nauchn. Sem. LOMI, 140 (1984), 105–122; J. Soviet Math., 32:2 (1986), 173–185
L. A. Molotkov, A. E. Khilo, “The effective media for periodic anisotropic systems”, Zap. Nauchn. Sem. LOMI, 128 (1983), 130–138
56.
L. A. Molotkov, A. E. Khilo, “She investigation of propagation of three-dimensional waves in stratified elastic and elasticfluid systems”, Zap. Nauchn. Sem. LOMI, 128 (1983), 116–129
57.
L. A. Molotkov, N. A. Razumovskii, “On the matrix method for slightly heterogeneous layered acoustical media”, Zap. Nauchn. Sem. LOMI, 128 (1983), 105–115
L. A. Molotkov, “A finite expression of characteristic matrices of slightly bent elastic layers”, Zap. Nauchn. Sem. LOMI, 104 (1981), 156–169; J. Soviet Math., 20:1 (1982), 1845–1854
L. A. Molotkov, U. Baimagambetov, “On the investigation of the roots of dispersion equation for layered transversal-isotropic medium”, Zap. Nauchn. Sem. LOMI, 99 (1980), 104–122; J. Soviet Math., 20:5 (1982), 2462–2475
60.
L. A. Molotkov, U. Baimagambetov, N. S. Smirnova, “On the investigation of the dispersion equation for the free transversal-isotropic elastic layer”, Zap. Nauchn. Sem. LOMI, 99 (1980), 85–103; J. Soviet Math., 20:5 (1982), 2448–2461
L. A. Molotkov, “On the characteristic matrices of the slightly bent elastic layers”, Zap. Nauchn. Sem. LOMI, 99 (1980), 74–84; J. Soviet Math., 20:5 (1982), 2441–2448
L. A. Molotkov, “On the equivalence between layer-periodic and transversal-isotropic media”, Zap. Nauchn. Sem. LOMI, 89 (1979), 219–233; J. Soviet Math., 19:4 (1982), 1454–1466
L. A. Molotkov, U. Baimagambetov, “Wave propagation in, layered, transversally isotropic, elastic media”, Zap. Nauchn. Sem. LOMI, 78 (1978), 149–173; J. Soviet Math., 22:1 (1983), 1098–1115
L. A. Molotkov, “Coefficients of reflection and refraction in the case of elastic-fluid systems”, Zap. Nauchn. Sem. LOMI, 62 (1976), 154–167; J. Soviet Math., 11:5 (1979), 763–771
L. A. Molotkov, “Damping of Rayleigh waves excited by a moving source”, Zap. Nauchn. Sem. LOMI, 62 (1976), 137–153; J. Soviet Math., 11:5 (1979), 752–762
1974
66.
L. A. Molotkov, “On the Dispfrlsion Equations of Vertically Inhomogenous Elastic and Liquid Media”, Zap. Nauchn. Sem. LOMI, 42 (1974), 189–211
1973
67.
L. A. Molotkov, “On the interference waves in the free heterogeneous elastic layer”, Zap. Nauchn. Sem. LOMI, 34 (1973), 117–141
68.
L. A. Molotkov, “On the dispersion equations of layered media with unhard contact on some boundaries”, Zap. Nauchn. Sem. LOMI, 34 (1973), 103–116
1972
69.
L. A. Molotkov, “On the matric representions of the dispersion equation for layer-elastic media”, Zap. Nauchn. Sem. LOMI, 25 (1972), 116–131
70.
P. V. Krauklis, L. A. Molotkov, “Low-frequency Lamb waves in cylindrical and spherical layers embedded in an elastic medium”, Zap. Nauchn. Sem. LOMI, 25 (1972), 101–110
1968
71.
L. A. Molotkov, “On the propagation of elastic waves from an irregularly moving source”, Trudy Mat. Inst. Steklov., 95 (1968), 132–150; Proc. Steklov Inst. Math., 95 (1968), 159–180
2004
72.
V. M. Babich, L. A. Molotkov, N. Ya. Kirpichnikova, “Pavel Vladimirovich Krauklis”, Zap. Nauchn. Sem. POMI, 308 (2004), 7–8; J. Math. Sci. (N. Y.), 132:1 (2006), 1
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