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Volumn 10, Issue 4, 2008, Pages 903-924

On a Hamiltonian PDE arising in magma dynamics

Author keywords

Compactons; Magma; Solitary waves; Stability; Variational methods; Viscously deformable porous media; Well posedness

Indexed keywords


EID: 57749169697     PISSN: 15313492     EISSN: None     Source Type: Journal    
DOI: 10.3934/dcdsb.2008.10.903     Document Type: Article
Times cited : (17)

References (36)
  • 1
    • 0024856665 scopus 로고
    • Solitary waves in magma dynamics
    • V. Barcilon and O. Lovera, Solitary waves in magma dynamics, J. Fluid Mech., 204 (1989), 121-133.
    • (1989) J. Fluid Mech , vol.204 , pp. 121-133
    • Barcilon, V.1    Lovera, O.2
  • 2
    • 0022674386 scopus 로고
    • Non-linear waves in compacting media
    • V. Barcilon and F. M. Richter, Non-linear waves in compacting media, J. Fluid Mech., 164 (1986), 429-448.
    • (1986) J. Fluid Mech , vol.164 , pp. 429-448
    • Barcilon, V.1    Richter, F.M.2
  • 5
    • 34249773260 scopus 로고
    • On the stability of solitary-wave solutions of model equations for long waves
    • J. L. Bona and A. Soyeur, On the stability of solitary-wave solutions of model equations for long waves, Journal of Nonlinear Science, 4 (1994), 449-470.
    • (1994) Journal of Nonlinear Science , vol.4 , pp. 449-470
    • Bona, J.L.1    Soyeur, A.2
  • 8
    • 0039658244 scopus 로고    scopus 로고
    • Conservation laws for a nonlinear wave equation
    • S. E. Harris, Conservation laws for a nonlinear wave equation, Nonlinearity, 9 (1996), 187-208.
    • (1996) Nonlinearity , vol.9 , pp. 187-208
    • Harris, S.E.1
  • 10
    • 0004148844 scopus 로고    scopus 로고
    • American Mathematical Society
    • E. H. Lieb and M. Loss, "Analysis," American Mathematical Society, 2001.
    • (2001) Analysis
    • Lieb, E.H.1    Loss, M.2
  • 11
    • 0021360880 scopus 로고
    • The generation and compaction of partially molten rock
    • D. McKenzie, The generation and compaction of partially molten rock, J. Petrol., 25 (1984), 713-765.
    • (1984) J. Petrol , vol.25 , pp. 713-765
    • McKenzie, D.1
  • 13
    • 0039066118 scopus 로고
    • Rarefactive solitary waves in two-phase fluid flow of compacting media
    • M. Nakayama and D. P. Mason, Rarefactive solitary waves in two-phase fluid flow of compacting media, Wave Motion, 15 (1992), 357-392.
    • (1992) Wave Motion , vol.15 , pp. 357-392
    • Nakayama, M.1    Mason, D.P.2
  • 14
    • 21344478000 scopus 로고
    • On the existence of compressive solitary waves in compacting media
    • M. Nakayama and D. P. Mason, On the existence of compressive solitary waves in compacting media, Journal of Physics A, 27 (1994), 4589-4599.
    • (1994) Journal of Physics A , vol.27 , pp. 4589-4599
    • Nakayama, M.1    Mason, D.P.2
  • 15
    • 0001009571 scopus 로고
    • Solitary wave propagation in a fluid conduit within a viscous matrix
    • P. Olson and U. Christensen, Solitary wave propagation in a fluid conduit within a viscous matrix, Journal of Geophysical Research, 91 (1986), 6367-6374.
    • (1986) Journal of Geophysical Research , vol.91 , pp. 6367-6374
    • Olson, P.1    Christensen, U.2
  • 17
    • 0003687441 scopus 로고
    • Methods of Modern Mathematical Physics I: Functional Analysis
    • Edition, Academic Press
    • Michael Reed and Barry Simon, "Methods of Modern Mathematical Physics I: Functional Analysis, Revised and Enlarged Edition," Academic Press, 1980.
    • (1980) Revised and Enlarged
    • Reed, M.1    Simon, B.2
  • 18
    • 33745206308 scopus 로고    scopus 로고
    • On a model equation of traveling and stationary compactons
    • P. Rosenau, On a model equation of traveling and stationary compactons, Physics Letters A, 356 (2006), 44-50.
    • (2006) Physics Letters A , vol.356 , pp. 44-50
    • Rosenau, P.1
  • 19
    • 12044253199 scopus 로고
    • Compactons - solitons with finite wavelength
    • P. Rosenau and J. M. Hyman, Compactons - solitons with finite wavelength, Physical Review Letters, 70 (1993), 564-567.
    • (1993) Physical Review Letters , vol.70 , pp. 564-567
    • Rosenau, P.1    Hyman, J.M.2
  • 22
    • 0001430244 scopus 로고
    • Magma ascent by porous flow
    • D. R. Scott and D. J. Stevenson, Magma ascent by porous flow, J. Geophys. Res., 91 (1986), 9283-9296.
    • (1986) J. Geophys. Res , vol.91 , pp. 9283-9296
    • Scott, D.R.1    Stevenson, D.J.2
  • 23
    • 0023041857 scopus 로고
    • Observations of solitary waves in a viscously deformable pipe
    • D. R. Scott, D. J. Stevenson, and J. A. Whitehead, Observations of solitary waves in a viscously deformable pipe, Nature, 319 (1986), 759-761.
    • (1986) Nature , vol.319 , pp. 759-761
    • Scott, D.R.1    Stevenson, D.J.2    Whitehead, J.A.3
  • 25
    • 33947625062 scopus 로고    scopus 로고
    • Degenerate dispersive equations arising in the stuyd of magma dynamics
    • G. Simpson, M. Spiegelman, and M. I. Weinstein, Degenerate dispersive equations arising in the stuyd of magma dynamics, Nonlinearity, 20 (2007), 21-49.
    • (2007) Nonlinearity , vol.20 , pp. 21-49
    • Simpson, G.1    Spiegelman, M.2    Weinstein, M.I.3
  • 27
    • 84974379685 scopus 로고
    • Flow in deformable porous media, part 1. Simple analysis
    • M. Spiegelman, Flow in deformable porous media, part 1. Simple analysis, J. Fluid Mech., 247 (1993), 17-38.
    • (1993) J. Fluid Mech , vol.247 , pp. 17-38
    • Spiegelman, M.1
  • 29
    • 0039066125 scopus 로고
    • Properties of the magma and modified magma equations
    • D. Takahashi, J. R. Sachs, and J. Satsuma, Properties of the magma and modified magma equations, J. Phys. Soc. Japan, 59 (1990), 1941-1953.
    • (1990) J. Phys. Soc. Japan , vol.59 , pp. 1941-1953
    • Takahashi, D.1    Sachs, J.R.2    Satsuma, J.3
  • 30
    • 0003704518 scopus 로고
    • Explicit solutions of magma equation
    • D. Takahashi and J. Satsuma, Explicit solutions of magma equation, J. Phys. Soc. Japan, 57 (1988), 417-421.
    • (1988) J. Phys. Soc. Japan , vol.57 , pp. 417-421
    • Takahashi, D.1    Satsuma, J.2
  • 31
    • 0000686130 scopus 로고
    • Modulational stability of ground states of nonlinear schrödinger equations
    • M. I. Weinstein, Modulational stability of ground states of nonlinear schrödinger equations, SIAM Journal of Mathematical Analysis, 16 (1985), 472-490.
    • (1985) SIAM Journal of Mathematical Analysis , vol.16 , pp. 472-490
    • Weinstein, M.I.1
  • 32
    • 84990553584 scopus 로고
    • Lyapunov stability of ground states of nonlinear dispersive evolution equations
    • M. I. Weinstein, Lyapunov stability of ground states of nonlinear dispersive evolution equations, Communications on Pure and Applied Mathematics, 39 (1986), 51-68.
    • (1986) Communications on Pure and Applied Mathematics , vol.39 , pp. 51-68
    • Weinstein, M.I.1
  • 33
    • 0011748760 scopus 로고
    • A laboratory demonstration of solitons using a vertical watery conduit in syrup
    • J. A. Whitehead, A laboratory demonstration of solitons using a vertical watery conduit in syrup, American Journal of Physics, 55 (1987), 998.
    • (1987) American Journal of Physics , vol.55 , pp. 998
    • Whitehead, J.A.1
  • 35
    • 0024226026 scopus 로고
    • Wave transport of deep mantle material
    • J. A. Whitehead and K. R. Helfrich, Wave transport of deep mantle material, Nature, 336 (1988), 59-61.
    • (1988) Nature , vol.336 , pp. 59-61
    • Whitehead, J.A.1    Helfrich, K.R.2
  • 36
    • 0028870883 scopus 로고
    • Magma migration and magmatic solitary waves in 3-d
    • Chris Wiggins and Marc Spiegelman, Magma migration and magmatic solitary waves in 3-d, Geophysical Research Letters, 22 (1995), 1289-1292.
    • (1995) Geophysical Research Letters , vol.22 , pp. 1289-1292
    • Wiggins, C.1    Spiegelman, M.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.