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Volumn 17, Issue 2, 1996, Pages 305-327

Moving mesh methods for problems with blow-up

Author keywords

Blow up solution; Moving mesh; Scaling invariance

Indexed keywords


EID: 0000458449     PISSN: 10648275     EISSN: None     Source Type: Journal    
DOI: 10.1137/S1064827594272025     Document Type: Article
Times cited : (159)

References (28)
  • 2
    • 0000355898 scopus 로고
    • Final time blowup profiles for semilinear parabolic equations via centre manifold theory
    • J. BEBERNES AND S. BRICHER, Final time blowup profiles for semilinear parabolic equations via centre manifold theory, SIAM J. Appl. Math., 23 (1992), pp. 852-869.
    • (1992) SIAM J. Appl. Math. , vol.23 , pp. 852-869
    • Bebernes, J.1    Bricher, S.2
  • 4
    • 0027608196 scopus 로고
    • Blowup in a parabolic equation with constraints, SIAM
    • C. J. BUDD, J. W. DOLD, AND A. M. STUART, Blowup in a parabolic equation with constraints, SIAM J. Appl. Math., 53 (1993), pp. 718-742.
    • (1993) J. Appl. Math. , vol.53 , pp. 718-742
    • Budd, C.J.1    Dold, J.W.2    Stuart, A.M.3
  • 5
    • 0003940756 scopus 로고
    • Mathematical Problems for Combustion Theory
    • Springer-Verlag
    • J. BEBERNES AND D. EBERLY, Mathematical Problems for Combustion Theory, Appl. Math. Sci., 83, Springer-Verlag, 1989.
    • (1989) Appl. Math. Sci. , vol.83
    • Bebernes, J.1    Eberly, D.2
  • 6
    • 5844391918 scopus 로고
    • Some applications of adaptive mesh refinement
    • J. E. Flaherty, P. J. Paslow, M. S. Shephard, and J. D. Vasilakis, eds., SIAM, Philadelphia
    • M. BERGER, Some applications of adaptive mesh refinement, Adaptive Methods for Partial Differential Equations, J. E. Flaherty, P. J. Paslow, M. S. Shephard, and J. D. Vasilakis, eds., SIAM, Philadelphia, 1989.
    • (1989) Adaptive Methods for Partial Differential Equations
    • Berger, M.1
  • 7
    • 85033846544 scopus 로고    scopus 로고
    • Critical diffusion exponents for blow-up in quasi-linear elliptic PDEs with exponential source
    • to appear
    • C. J. BUDD AND V. A. GALAKTIONOV, Critical diffusion exponents for blow-up in quasi-linear elliptic PDEs with exponential source, Proc. Roy. Soc. Edinb., to appear.
    • Proc. Roy. Soc. Edinb.
    • Budd, C.J.1    Galaktionov, V.A.2
  • 8
    • 84990610650 scopus 로고
    • A rescaling algorithm for the numerical calculation of blowing-up solutions
    • M. BERGER AND R. V. KOHN, A rescaling algorithm for the numerical calculation of blowing-up solutions, Comm. Pure Appl. Math., 41 (1988), pp. 841-863.
    • (1988) Comm. Pure Appl. Math. , vol.41 , pp. 841-863
    • Berger, M.1    Kohn, R.V.2
  • 9
    • 84980149255 scopus 로고
    • Estimates of intermittency, spectra, and blow-up in developed turbulence
    • A. J. CHORIN, Estimates of intermittency, spectra, and blow-up in developed turbulence, Comm. Pure Appl. Math., 34 (1981), pp. 853-866.
    • (1981) Comm. Pure Appl. Math. , vol.34 , pp. 853-866
    • Chorin, A.J.1
  • 10
    • 0001121137 scopus 로고
    • Simple adaptive grids for 1-D initial value problems
    • E. A. DORFI AND L. O'C. DRURY, Simple adaptive grids for 1-D initial value problems, J. Comp. Phys., 69 (1987), pp. 175-195.
    • (1987) J. Comp. Phys. , vol.69 , pp. 175-195
    • Dorfi, E.A.1    Drury, L.O'C.2
  • 11
    • 0022113843 scopus 로고
    • Analysis of the early stage of thermal runaway
    • J. W. DOLD, Analysis of the early stage of thermal runaway, Quart. J. Mech. Appl. Math., 38 (1985), pp. 361-387.
    • (1985) Quart. J. Mech. Appl. Math. , vol.38 , pp. 361-387
    • Dold, J.W.1
  • 13
    • 0002259684 scopus 로고
    • Blow-up at the boundary for degenerate semilinear parabolic equations
    • M. S. FLOATER, Blow-up at the boundary for degenerate semilinear parabolic equations, Arch. Rational Mech. Anal., 114 (1991), pp. 57-77.
    • (1991) Arch. Rational Mech. Anal. , vol.114 , pp. 57-77
    • Floater, M.S.1
  • 14
    • 0000546335 scopus 로고
    • Blow up of positive solutions of semilinear heat equations
    • A. FRIEDMAN AND B. MCLEOD, Blow up of positive solutions of semilinear heat equations, Indiana Univ. Math. J., 34 (1985), pp. 425-447.
    • (1985) Indiana Univ. Math. J. , vol.34 , pp. 425-447
    • Friedman, A.1    Mcleod, B.2
  • 15
    • 0001367417 scopus 로고
    • A numerical study of three moving grid methods for one-dimensional partial differential equations which are based on the method of lines
    • R. M. FURZELAND, J. G. VERWER, AND P. A. ZEGELING, A numerical study of three moving grid methods for one-dimensional partial differential equations which are based on the method of lines, J. Comp. Phys., 89 (1990), pp. 349-388.
    • (1990) J. Comp. Phys. , vol.89 , pp. 349-388
    • Furzeland, R.M.1    Verwer, J.G.2    Zegeling, P.A.3
  • 16
    • 0000247179 scopus 로고
    • Some problems in the theory of quasilinear equations
    • I. M. GELFAND, Some problems in the theory of quasilinear equations, Amer. Math. Soc. Trans., 29 (1963), pp. 295-381.
    • (1963) Amer. Math. Soc. Trans. , vol.29 , pp. 295-381
    • Gelfand, I.M.1
  • 17
    • 84990616610 scopus 로고
    • Asymptotically self-similar blowup of semilinear heat equations
    • Y. GIGA AND R. KOHN, Asymptotically self-similar blowup of semilinear heat equations, Comm. Pure Appl. Math., 38 (1985), pp. 297-319.
    • (1985) Comm. Pure Appl. Math. , vol.38 , pp. 297-319
    • Giga, Y.1    Kohn, R.2
  • 18
    • 0039936971 scopus 로고
    • Single point blow-up for N-dimensional quasilinear equations with gradient diffusion and source
    • V. A. GALAKTIONOV AND S. A. POSASHKOV, Single point blow-up for N-dimensional quasilinear equations with gradient diffusion and source, Indiana Univ. Math. J., 40 (1991), pp. 1041-1060.
    • (1991) Indiana Univ. Math. J. , vol.40 , pp. 1041-1060
    • Galaktionov, V.A.1    Posashkov, S.A.2
  • 20
    • 0028446372 scopus 로고
    • Moving mesh partial differential equations (MMPDEs) based on the equidistribution principle
    • W. HUANG, Y. REN, AND R. D. RUSSELL, Moving mesh partial differential equations (MMPDEs) based on the equidistribution principle, SIAM J. Numer. Anal., 31 (1994), pp. 709-730.
    • (1994) SIAM J. Numer. Anal. , vol.31 , pp. 709-730
    • Huang, W.1    Ren, Y.2    Russell, R.D.3
  • 21
    • 0000105971 scopus 로고
    • Moving mesh methods based upon moving mesh partial differential equations
    • _, Moving mesh methods based upon moving mesh partial differential equations, J. Comp. Phys., 113 (1994), pp. 279-290.
    • (1994) J. Comp. Phys. , vol.113 , pp. 279-290
  • 22
    • 85011578583 scopus 로고
    • Blow-up behaviour for one-dimensional semilinear parabolic equations
    • M. HERRERO AND J. VELAZQUEZ, Blow-up behaviour for one-dimensional semilinear parabolic equations, Ann. Inst. H. Poincaré, Analyse nonlinéaire, 10 (1993), pp. 131-189.
    • (1993) Ann. Inst. H. Poincaré, Analyse Nonlinéaire , vol.10 , pp. 131-189
    • Herrero, M.1    Velazquez, J.2
  • 23
    • 0041047951 scopus 로고
    • Dynamic rezone methods for partial differential equations in one space dimension
    • J. M. HYMAN AND B. LARROUTUROU, Dynamic rezone methods for partial differential equations in one space dimension, Appl. Numer. Math., 5 (1989), pp. 435-450.
    • (1989) Appl. Numer. Math. , vol.5 , pp. 435-450
    • Hyman, J.M.1    Larrouturou, B.2
  • 24
    • 0017459198 scopus 로고
    • The supercritical spatially homogeneous thermal explosion: Initiation to completion
    • D. KASSOY, The supercritical spatially homogeneous thermal explosion: Initiation to completion, Quart. J. Mech. Appl. Math., 30 (1977), pp. 71-89.
    • (1977) Quart. J. Mech. Appl. Math. , vol.30 , pp. 71-89
    • Kassoy, D.1
  • 25
    • 35949022121 scopus 로고
    • The focusing singularity of the nonlinear Schrödinger equation
    • B. LEMESURIER, G. PAPANICOLAOU, C. SULEM, AND P.-L. SULEM, The focusing singularity of the nonlinear Schrödinger equation, Phys. Rev. A, 34 (1986), pp. 1200-1210.
    • (1986) Phys. Rev. A , vol.34 , pp. 1200-1210
    • Lemesurier, B.1    Papanicolaou, G.2    Sulem, C.3    Sulem, P.-L.4
  • 28
    • 0004456294 scopus 로고
    • A moving grid method for one-dimensional PDEs based on the method of lines
    • J. E. Flaherty, P. J. Paslow, M. S. Shephard, and J. D. Vasilakis, eds., SIAM, Philadelphia
    • J. G. VERWER, J. G. BLOM, R. M. FURZELAND, AND P. A. ZEGELING, A moving grid method for one-dimensional PDEs based on the method of lines, Adaptive Methods for Partial Differential Equations, J. E. Flaherty, P. J. Paslow, M. S. Shephard, and J. D. Vasilakis, eds., SIAM, Philadelphia, 1989.
    • (1989) Adaptive Methods for Partial Differential Equations
    • Verwer, J.G.1    Blom, J.G.2    Furzeland, R.M.3    Zegeling, P.A.4


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.