메뉴 건너뛰기




Volumn , Issue 545, 2002, Pages 19-65

Pointwise estimates and stability for degenerate viscous shock waves

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0036253930     PISSN: 00754102     EISSN: None     Source Type: Journal    
DOI: 10.1515/crll.2002.034     Document Type: Article
Times cited : (27)

References (53)
  • 1
    • 0005235678 scopus 로고
    • A topological invariant arising in the analysis of traveling waves
    • [AGJ]
    • [AGJ] J. Alexander, R. Gardner, and C. K. R. T. Jones, A topological invariant arising in the analysis of traveling waves, J. reine angew. Math. 410 (1990), 167-212.
    • (1990) J. Reine Angew. Math. , vol.410 , pp. 167-212
    • Alexander, J.1    Gardner, R.2    Jones, C.K.R.T.3
  • 4
    • 0004165280 scopus 로고
    • [F], Springer-Verlag, Berlin-Heidelberg
    • [F] M. V. Fedoryuk, Asymptotic analysis, Springer-Verlag, Berlin-Heidelberg 1993.
    • (1993) Asymptotic Analysis
    • Fedoryuk, M.V.1
  • 5
    • 0004064379 scopus 로고
    • [FD], University of California Press, London
    • [FD] W. Fickett and W. C. Davis, Detonation, University of California Press, London 1979.
    • (1979) Detonation
    • Fickett, W.1    Davis, W.C.2
  • 6
    • 0040942605 scopus 로고    scopus 로고
    • The Gap Lemma and geometric criteria for instability of viscous shock profiles
    • [GZ]
    • [GZ] R. Gardner and K. Zumbrun, The Gap Lemma and geometric criteria for instability of viscous shock profiles, CPAM 51 (1998), 789-847.
    • (1998) CPAM , pp. 789-847
    • Gardner, R.1    Zumbrun, K.2
  • 7
    • 0022865466 scopus 로고
    • Nonlinear asymptotic stability of viscous shock profiles for conservation laws
    • [G]
    • [G] J. Goodman, Nonlinear asymptotic stability of viscous shock profiles for conservation laws, Arch. Rat. Mech. Anal. 95 (1986), 325-344.
    • (1986) Arch. Rat. Mech. Anal. , vol.95 , pp. 325-344
    • Goodman, J.1
  • 8
    • 0030502109 scopus 로고    scopus 로고
    • Sonic shocks governed by the modified Burgers' equation
    • [Ha]
    • [Ha] S. E. Harris, Sonic shocks governed by the modified Burgers' equation, Euro. J. Appl. Math. 7 (1996), 201-222.
    • (1996) Euro. J. Appl. Math. , vol.7 , pp. 201-222
    • Harris, S.E.1
  • 11
    • 84980078224 scopus 로고
    • xx
    • [H]
    • xx, CPAM 3 (1950), 201-230.
    • (1950) CPAM , vol.3 , pp. 201-230
    • Hopf, E.1
  • 13
    • 0033164375 scopus 로고    scopus 로고
    • Pointwise estimates on the Green's function for a scalar linear convection-diffusion equation
    • [H2]
    • [H2] P. Howard, Pointwise estimates on the Green's function for a scalar linear convection-diffusion equation, J. Diff. Equ. 155 (1999), 327-367.
    • (1999) J. Diff. Equ. , vol.155 , pp. 327-367
    • Howard, P.1
  • 14
    • 0033441053 scopus 로고    scopus 로고
    • Pointwise Green's function approach to stability for scalar conservation laws
    • [H3]
    • [H3] P. Howard, Pointwise Green's function approach to stability for scalar conservation laws, CPAM 52 (1999), 1295-1313.
    • (1999) CPAM , vol.52 , pp. 1295-1313
    • Howard, P.1
  • 17
    • 0002609897 scopus 로고    scopus 로고
    • Asymptotic decay toward planar rarefaction waves of solutions for viscous conservation laws in several space dimensions
    • [Ito]
    • [Ito] K. Ito, Asymptotic decay toward planar rarefaction waves of solutions for viscous conservation laws in several space dimensions, Math. Models Meth. Appl. Sci. 6 (1996), 315-338.
    • (1996) Math. Models Meth. Appl. Sci. , vol.6 , pp. 315-338
    • Ito, K.1
  • 18
    • 84990556253 scopus 로고
    • Stability of traveling waves for nonconvex scalar viscous conservation laws
    • [JGK]
    • [JGK] C. K. R. T. Jones, R. Gardner, and T. Kapitula, Stability of traveling waves for nonconvex scalar viscous conservation laws, CPAM 46 (1993), no. 4, 505-526.
    • (1993) CPAM , vol.46 , Issue.4 , pp. 505-526
    • Jones, C.K.R.T.1    Gardner, R.2    Kapitula, T.3
  • 19
    • 0033628312 scopus 로고    scopus 로고
    • Existence and stability of standing hole solutions to complex Ginzburg-Landau equations
    • [KR]
    • [KR] T. Kapitula and J. Rubin, Existence and stability of standing hole solutions to complex Ginzburg-Landau equations, Nonlin. 13 (2000), no. 1, 77-112.
    • (2000) Nonlin. , vol.13 , Issue.1 , pp. 77-112
    • Kapitula, T.1    Rubin, J.2
  • 20
    • 0002348145 scopus 로고    scopus 로고
    • Stability of bright solitary-wave solutions to perturbed nonlinear Schrödinger equations
    • [KS]
    • [KS] T. Kapitula and B. Sandstede, Stability of bright solitary-wave solutions to perturbed nonlinear Schrödinger equations, Physica D 124 (1998), 58-103.
    • (1998) Physica D , vol.124 , pp. 58-103
    • Kapitula, T.1    Sandstede, B.2
  • 21
    • 34250115323 scopus 로고
    • Asymptotic stability of traveling wave solutions of systems for one-dimensional gas motion
    • [KM1]
    • [KM1] S. Kawashima and A. Matsumura, Asymptotic stability of traveling wave solutions of systems for one-dimensional gas motion, Comm. Math. Phys. 101 (1985), 97-127.
    • (1985) Comm. Math. Phys. , vol.101 , pp. 97-127
    • Kawashima, S.1    Matsumura, A.2
  • 22
    • 62449235559 scopus 로고
    • Stability of shock profiles in viscoelasticity with non-convex constitution relations
    • [KM2]
    • [KM2] S. Kawashima and A. Matsumura, Stability of shock profiles in viscoelasticity with non-convex constitution relations, CPAM 47 (1994), 1547-1569.
    • (1994) CPAM , vol.47 , pp. 1547-1569
    • Kawashima, S.1    Matsumura, A.2
  • 23
    • 84972530643 scopus 로고
    • The asymptotic nature of solutions of linear systems of differential equations
    • [Le]
    • [Le] N. Levinson, The asymptotic nature of solutions of linear systems of differential equations, Duke Math. J. 15 (1948), 111-126.
    • (1948) Duke Math. J. , vol.15 , pp. 111-126
    • Levinson, N.1
  • 24
    • 0000138333 scopus 로고
    • On the initiation problem for a combustion model
    • [Li1]
    • [Li1] T. Li, On the initiation problem for a combustion model, J. Diff. Equ. 112 (1994), no. 2, 351-373.
    • (1994) J. Diff. Equ. , vol.112 , Issue.2 , pp. 351-373
    • Li, T.1
  • 25
    • 0000249989 scopus 로고    scopus 로고
    • Rigorous asymptotic stability of a CJ detonation wave in the limit of small resolved heat release
    • [Li2]
    • [Li2] T. Li, Rigorous asymptotic stability of a CJ detonation wave in the limit of small resolved heat release, Combust. Th. Modell. 1 (1997), 259-270.
    • (1997) Combust. Th. Modell. , vol.1 , pp. 259-270
    • Li, T.1
  • 26
    • 0002840914 scopus 로고    scopus 로고
    • Stability of strong detonation waves and rates of convergence
    • [Li3]
    • [Li3] T. Li, Stability of strong detonation waves and rates of convergence, Electr. J. Diff. Equ. 1998 (1998), no. 9, 1-17.
    • (1998) Electr. J. Diff. Equ. , vol.1998 , Issue.9 , pp. 1-17
    • Li, T.1
  • 28
    • 84968504658 scopus 로고
    • Nonlinear stability of shock waves for viscous conservation laws
    • [L]
    • [L] T.-P. Liu, Nonlinear stability of shock waves for viscous conservation laws, Mem. AMS 56 (1985), no. 328.
    • (1985) Mem. AMS , vol.56 , Issue.328
    • Liu, T.-P.1
  • 29
    • 0041429241 scopus 로고
    • Nonlinear stability of strong detonations for a viscous combustion model
    • [LY]
    • [LY] T.-P. Liu and L. A. Ying, Nonlinear stability of strong detonations for a viscous combustion model, SIAM J. Math. Anal. 26 (1995), 519-528.
    • (1995) SIAM J. Math. Anal. , vol.26 , pp. 519-528
    • Liu, T.-P.1    Ying, L.A.2
  • 30
    • 0019599446 scopus 로고
    • A qualitative model for dynamics combustion
    • [M]
    • [M] A. Majda, A qualitative model for dynamics combustion, SIAM J. ppl. Math. 41 (1981), 70-93.
    • (1981) SIAM J. Appl. Math. , vol.41 , pp. 70-93
    • Majda, A.1
  • 31
    • 0001923997 scopus 로고
    • On the stability of traveling wave solutions of a one-dimensional model system for compressive viscous gas
    • [MN1]
    • [MN1] A. Matsumura and K. Nishihara, On the stability of traveling wave solutions of a one-dimensional model system for compressive viscous gas, Japan. J. Appl. Math. 2 (1985), 17-25.
    • (1985) Japan. J. Appl. Math. , vol.2 , pp. 17-25
    • Matsumura, A.1    Nishihara, K.2
  • 32
    • 0001790393 scopus 로고
    • Asymptotics toward the rarefaction waves of the solutions of a one-dimensional model system for compressible viscous gas
    • [MN2]
    • [MN2] A. Matsumura and K. Nishihara, Asymptotics toward the rarefaction waves of the solutions of a one-dimensional model system for compressible viscous gas, Japan. J. Appl. Math. 3 (1986), 1-13.
    • (1986) Japan. J. Appl. Math. , vol.3 , pp. 1-13
    • Matsumura, A.1    Nishihara, K.2
  • 33
    • 34249841641 scopus 로고
    • Global stability of the rarefaction wave of a one-dimensional model system for compressible viscous gas
    • [MN3]
    • [MN3] A. Matsumura and K. Nishihara, Global stability of the rarefaction wave of a one-dimensional model system for compressible viscous gas, Comm. Math. Phys. 144 (1992), 325-335.
    • (1992) Comm. Math. Phys. , vol.144 , pp. 325-335
    • Matsumura, A.1    Nishihara, K.2
  • 34
    • 21844512198 scopus 로고
    • Asymptotic stability of traveling waves for scalar viscous conservation laws with non-convex linearity
    • [MN4]
    • [MN4] A. Matsumura and K. Nishihara, Asymptotic stability of traveling waves for scalar viscous conservation laws with non-convex linearity, Comm. Math. Phys. 165 (1994), no. 1, 83-96.
    • (1994) Comm. Math. Phys. , vol.165 , Issue.1 , pp. 83-96
    • Matsumura, A.1    Nishihara, K.2
  • 35
    • 0033886978 scopus 로고    scopus 로고
    • Global asymptotics toward the rarefaction wave for solutions of viscous p-systems with boundary effect
    • [MN5]
    • [MN5] A. Matsumura and K. Nishihara, Global asymptotics toward the rarefaction wave for solutions of viscous p-systems with boundary effect, Quart. Appl. Math. 58 (2000), no. 1, 69-83.
    • (2000) Quart. Appl. Math. , vol.58 , Issue.1 , pp. 69-83
    • Matsumura, A.1    Nishihara, K.2
  • 36
    • 0009377159 scopus 로고
    • Stability of shock profiles for nonconvex scalar viscous conservation laws
    • [M1]
    • [M1] M. Mei, Stability of shock profiles for nonconvex scalar viscous conservation laws, Math. Models Meth. Appl. Sci. 5 (1995), no. 3, 279-296.
    • (1995) Math. Models Meth. Appl. Sci. , vol.5 , Issue.3 , pp. 279-296
    • Mei, M.1
  • 37
    • 0040151449 scopus 로고    scopus 로고
    • Stability of traveling wave solutions for non-convex equations of barotropic viscous gas
    • [M2]
    • [M2] M. Mei, Stability of traveling wave solutions for non-convex equations of barotropic viscous gas, Osaka J. Math. 34 (1997), 308-318.
    • (1997) Osaka J. Math. , vol.34 , pp. 308-318
    • Mei, M.1
  • 38
    • 0033245877 scopus 로고    scopus 로고
    • Asymptotic behavior of solutions for degenerate hyperbolic systems of viscous conservation laws with boundary effect
    • [M3]
    • [M3] M. Mei, Asymptotic behavior of solutions for degenerate hyperbolic systems of viscous conservation laws with boundary effect, ZAMP 50 (1999), 617-633.
    • (1999) ZAMP , vol.50 , pp. 617-633
    • Mei, M.1
  • 39
    • 0009173909 scopus 로고    scopus 로고
    • Nonlinear stability of traveling waves for one-dimensional viscoelastic materials with non-convex nonlinearity
    • [MeiN]
    • [MeiN] M. Mei and K. Nishihara, Nonlinear stability of traveling waves for one-dimensional viscoelastic materials with non-convex nonlinearity, Tokyo J. Math. 20 (1997), no. 1, 241-264.
    • (1997) Tokyo J. Math. , vol.20 , Issue.1 , pp. 241-264
    • Mei, M.1    Nishihara, K.2
  • 41
    • 0010564672 scopus 로고
    • A note on the stability of traveling wave solutions of Burgers equation
    • [N1]
    • [N1] K. Nishihara, A note on the stability of traveling wave solutions of Burgers equation, Japan. J. Appl. Math. 2 (1985), 27-35.
    • (1985) Japan. J. Appl. Math. , vol.2 , pp. 27-35
    • Nishihara, K.1
  • 42
    • 0000158254 scopus 로고
    • Stability of traveling waves with degenerate shock for system of one-dimensional viscoelastic model
    • [N2]
    • [N2] K. Nishihara, Stability of traveling waves with degenerate shock for system of one-dimensional viscoelastic model, J. Diff. Equ. 120 (1995), 304-318.
    • (1995) J. Diff. Equ. , vol.120 , pp. 304-318
    • Nishihara, K.1
  • 43
    • 0001293121 scopus 로고    scopus 로고
    • Convergence rate to the traveling wave for viscous conservation laws
    • [Ni]
    • [Ni] M. Nishikawa, Convergence rate to the traveling wave for viscous conservation laws, Funkcialoj Ekvacioj 41 (1998), 107-132.
    • (1998) Funkcialoj Ekvacioj , vol.41 , pp. 107-132
    • Nishikawa, M.1
  • 44
    • 0020830109 scopus 로고
    • Weakly nonlinear detonation waves
    • [RM]
    • [RM] R. R. Rosales and A. Majda, Weakly nonlinear detonation waves, SIAM J. Appl. Math. 43 (1983), 10086-1118.
    • (1983) SIAM J. Appl. Math. , vol.43 , pp. 10086-11118
    • Rosales, R.R.1    Majda, A.2
  • 45
    • 0000814275 scopus 로고
    • On the stability of waves of nonlinear parabolic systems
    • [S]
    • [S] D. Sattinger, On the stability of waves of nonlinear parabolic systems, Adv. Math. 22 (1976), 312-355.
    • (1976) Adv. Math. , vol.22 , pp. 312-355
    • Sattinger, D.1
  • 46
    • 0030533740 scopus 로고    scopus 로고
    • Stability and rarefaction waves in viscous media
    • [SZ]
    • [SZ] A. Szepessy and K. Zumbrun, Stability and rarefaction waves in viscous media, Arch. Rat. Mech. Anal. 133 (1996), 249-298.
    • (1996) Arch. Rat. Mech. Anal. , vol.133 , pp. 249-298
    • Szepessy, A.1    Zumbrun, K.2
  • 47
    • 21344482836 scopus 로고
    • Transition to detonation in dynamic phase changes
    • [T]
    • [T] L. Truskinovsky, Transition to detonation in dynamic phase changes, Arch. Rat. Mech. Anal. 125 (1994), 375-397.
    • (1994) Arch. Rat. Mech. Anal. , vol.125 , pp. 375-397
    • Truskinovsky, L.1
  • 48
    • 0042287924 scopus 로고
    • Formation of diffusion waves in a scalar conservation law with convection
    • [Z1]
    • [Z1] K. Zumbrun, Formation of diffusion waves in a scalar conservation law with convection, Trans. Amer. Math. Soc. 347 (1995), no. 3, 1023-1032.
    • (1995) Trans. Amer. Math. Soc. , vol.347 , Issue.3 , pp. 1023-1032
    • Zumbrun, K.1
  • 50
    • 0043290030 scopus 로고    scopus 로고
    • [Z3]
    • [Z3] K. Zumbrun, Lecture notes, 1999, available on: http://www.math.indiana.edu/home/zumbrun.
    • (1999) Lecture Notes
    • Zumbrun, K.1
  • 52
    • 0009378734 scopus 로고    scopus 로고
    • Pointwise semigroup methods and stability of viscous shock waves
    • [ZH]
    • [ZH] K. Zumbrun and P. Howard, Pointwise semigroup methods and stability of viscous shock waves, Indiana U. Math. J. 47 (1998), no. 3, 741-871.
    • (1998) Indiana U. Math. J. , vol.47 , Issue.3 , pp. 741-871
    • Zumbrun, K.1    Howard, P.2
  • 53
    • 0001028485 scopus 로고    scopus 로고
    • Viscous and inviscid stability of multi-dimensional planar shock fronts
    • [ZS]
    • [ZS] K. Zumbrun and D. Serre, Viscous and inviscid stability of multi-dimensional planar shock fronts, Indiana Univ. Math. J. 48 (1999), no. 3, 937-992.
    • (1999) Indiana Univ. Math. J. , vol.48 , Issue.3 , pp. 937-992
    • Zumbrun, K.1    Serre, D.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.