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Volumn 128, Issue 5, 1998, Pages 965-992

Focusing blow-up for quasilinear parabolic equations

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EID: 22444451936     PISSN: 03082105     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0308210500030018     Document Type: Article
Times cited : (16)

References (33)
  • 1
    • 0043101398 scopus 로고
    • Absence of blowing up similarity structures in a medium with a source for constant thermal conductivity
    • in Russian
    • M. M. Ad'jutov and L. A. Lepin. Absence of blowing up similarity structures in a medium with a source for constant thermal conductivity. Differentsial'nye Uravneniya 20 (1984), 1279-81 [in Russian].
    • (1984) Differentsial'nye Uravneniya , vol.20 , pp. 1279-1281
    • Ad'jutov, M.M.1    Lepin, L.A.2
  • 4
    • 0001559570 scopus 로고
    • Asymptotics of blow-up for weakly quasilinear parabolic equations
    • J. Berbernes, S. Bricher and V. A. Galaktionov. Asymptotics of blow-up for weakly quasilinear parabolic equations. Nonlinear Anal. 23 (1994), 489-514.
    • (1994) Nonlinear Anal. , vol.23 , pp. 489-514
    • Berbernes, J.1    Bricher, S.2    Galaktionov, V.A.3
  • 5
    • 21344460450 scopus 로고    scopus 로고
    • Critical diffusion exponents for self-similar blow-up solutions of a quasilinear parabolic equation with an exponential source
    • C. J. Budd and V. A. Galaktionov. Critical diffusion exponents for self-similar blow-up solutions of a quasilinear parabolic equation with an exponential source. Proc. Roy. Soc. Edinburgh Sect. A 126 (1996), 413-41.
    • (1996) Proc. Roy. Soc. Edinburgh Sect. A , vol.126 , pp. 413-441
    • Budd, C.J.1    Galaktionov, V.A.2
  • 6
    • 0002610231 scopus 로고
    • Moving mesh methods with applications to blow-up problems for PDEs
    • Numerical Analysis 1995, Harlow: Longman
    • C. J. Budd, J. Chen, W. Huang and R. D. Russell. Moving mesh methods with applications to blow-up problems for PDEs. In Numerical Analysis 1995, Pitman Research Notes in Mathematics 44, pp. 1-18 (Harlow: Longman, 1995).
    • (1995) Pitman Research Notes in Mathematics 44 , pp. 1-18
    • Budd, C.J.1    Chen, J.2    Huang, W.3    Russell, R.D.4
  • 7
    • 0040984180 scopus 로고    scopus 로고
    • Self-similar blow-up for a quasilinear parabolic equation with gradient diffusion and exponential source
    • C. J. Budd, B. Dold and V. A. Galaktionov. Self-similar blow-up for a quasilinear parabolic equation with gradient diffusion and exponential source. Adv. Differential Equations 2 (1997), 85-124.
    • (1997) Adv. Differential Equations , vol.2 , pp. 85-124
    • Budd, C.J.1    Dold, B.2    Galaktionov, V.A.3
  • 8
    • 0000458449 scopus 로고    scopus 로고
    • Moving mesh methods for problems with blow-up
    • C. J. Budd, W. Huang and R. D. Russell. Moving mesh methods for problems with blow-up. SIAM J. Sci. Comp. 17 (1996), 305-27.
    • (1996) SIAM J. Sci. Comp. , vol.17 , pp. 305-327
    • Budd, C.J.1    Huang, W.2    Russell, R.D.3
  • 9
    • 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. Comput. Phys. 69 (1987), 175-95.
    • (1987) J. Comput. Phys. , vol.69 , pp. 175-195
    • Dorfi, E.A.1    O'C Drury, L.2
  • 11
    • 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), 57-77.
    • (1991) Arch. Rational Mech. Anal. , vol.114 , pp. 57-77
    • Floater, M.S.1
  • 12
    • 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), 425-47.
    • (1985) Indiana Univ. Math. J. , vol.34 , pp. 425-447
    • Friedman, A.1    McLeod, B.2
  • 13
    • 0038525448 scopus 로고
    • On asymptotic self-similar behaviour for a quasilinear heat equation: Single point blow-up
    • V. A. Galaktionov. On asymptotic self-similar behaviour for a quasilinear heat equation: single point blow-up. SIAM J. Math. Anal. 29 (1995), 675-93.
    • (1995) SIAM J. Math. Anal. , vol.29 , pp. 675-693
    • Galaktionov, V.A.1
  • 14
    • 85034196871 scopus 로고    scopus 로고
    • Asymptotic behaviour near finite time extinction for the fast diffusion equation
    • to appear
    • V. A. Galaktionov and L. A. Peletier. Asymptotic behaviour near finite time extinction for the fast diffusion equation. Arch. Rational Mech. Anal. (to appear).
    • Arch. Rational Mech. Anal.
    • Galaktionov, V.A.1    Peletier, L.A.2
  • 16
    • 0001457899 scopus 로고
    • Application of new comparison theorem in the investigation of unbounded solutions of nonlinear parabolic equations
    • V. A. Galaktionov and S. A. Posashkov. Application of new comparison theorem in the investigation of unbounded solutions of nonlinear parabolic equations. Differential Equations 22 (1986), 809-15.
    • (1986) Differential Equations , vol.22 , pp. 809-815
    • Galaktionov, V.A.1    Posashkov, S.A.2
  • 17
    • 0000005348 scopus 로고
    • Extinction for a quasilinear heat equation with absorption II. A dynamical systems approach
    • V. A. Galaktionov and J. L. Vazquez. Extinction for a quasilinear heat equation with absorption II. A dynamical systems approach. Comm. Partial Differential Equations 19 (1994). 1107-37.
    • (1994) Comm. Partial Differential Equations , vol.19 , pp. 1107-1137
    • Galaktionov, V.A.1    Vazquez, J.L.2
  • 18
    • 84990616610 scopus 로고
    • Asymptotically self-similar blow-up of semilinear heat equations
    • Y. Giga and R. V. Kohn. Asymptotically self-similar blow-up of semilinear heat equations. Comm. Pure Appl. Math. 38 (1985), 297-319.
    • (1985) Comm. Pure Appl. Math. , vol.38 , pp. 297-319
    • Giga, Y.1    Kohn, R.V.2
  • 19
    • 0000332576 scopus 로고
    • Characterizing blow-up using similarity variables
    • Y. Giga and R. V. Kohn. Characterizing blow-up using similarity variables. Indiana Univ. Math. J. 36 (1987), 1-40.
    • (1987) Indiana Univ. Math. J. , vol.36 , pp. 1-40
    • Giga, Y.1    Kohn, R.V.2
  • 21
    • 84959615928 scopus 로고
    • A non-linear instability burst in plane parallel flow
    • L. M. Hocking, K. Stuartson and J. T. Stuart. A non-linear instability burst in plane parallel flow. J. Fluid Mech. 51 (1972), 705-35.
    • (1972) J. Fluid Mech. , vol.51 , pp. 705-735
    • Hocking, L.M.1    Stuartson, K.2    Stuart, J.T.3
  • 22
    • 0030081518 scopus 로고    scopus 로고
    • A moving collocation method for solving time dependent partial differential equations
    • W.-Z. Huang and R. D. R. Russell. A moving collocation method for solving time dependent partial differential equations. Appl. Numer. Math. 20 (1996), 101-16.
    • (1996) Appl. Numer. Math. , vol.20 , pp. 101-116
    • Huang, W.-Z.1    Russell, R.D.R.2
  • 23
    • 0000105971 scopus 로고
    • Moving mesh methods based on moving mesh partial differential equations
    • W.-Z. Huang, Y. Ren and R. D. R. Russell. Moving mesh methods based on moving mesh partial differential equations. J. Comput. Phys. 113 (1994), 279-90.
    • (1994) J. Comput. Phys. , vol.113 , pp. 279-290
    • Huang, W.-Z.1    Ren, Y.2    Russell, R.D.R.3
  • 24
    • 84862599035 scopus 로고
    • Some problems of the qualitative theory of non-linear degenerate second-order parabolic equations
    • A. S. Kalashnikov. Some problems of the qualitative theory of non-linear degenerate second-order parabolic equations. Russian Math. Surveys 42 (1987), 169-222.
    • (1987) Russian Math. Surveys , vol.42 , pp. 169-222
    • Kalashnikov, A.S.1
  • 25
    • 84980186071 scopus 로고
    • Non-linear diffusion in a finite mass medium
    • S. Kamin and P. Rosenau. Non-linear diffusion in a finite mass medium. Comm. Pure Appl. Math. 35 (1982), 113-27.
    • (1982) Comm. Pure Appl. Math. , vol.35 , pp. 113-127
    • Kamin, S.1    Rosenau, P.2
  • 26
    • 84971178534 scopus 로고
    • The form of blow-up for nonlinear parabolic equations
    • A. A. Lacey. The form of blow-up for nonlinear parabolic equations. Proc. Roy. Soc. Edinburgh Sect. A 98 (1984), 183-202.
    • (1984) Proc. Roy. Soc. Edinburgh Sect. A , vol.98 , pp. 183-202
    • Lacey, A.A.1
  • 27
    • 0018323228 scopus 로고
    • Channel flows with temperature-dependent viscosity and internal viscous dissipation
    • H. Ockendon. Channel flows with temperature-dependent viscosity and internal viscous dissipation. J. Fluid Mech. 93 (1979), 737-46.
    • (1979) J. Fluid Mech. , vol.93 , pp. 737-746
    • Ockendon, H.1
  • 29
    • 0000514956 scopus 로고
    • Eigenfunction of the equation Δu + λf(u) = 0
    • S. I. Pohozaev. Eigenfunction of the equation Δu + λf(u) = 0. Soviet Math. Dokl. 6 (1965), 1408-11.
    • (1965) Soviet Math. Dokl. , vol.6 , pp. 1408-1411
    • Pohozaev, S.I.1
  • 32
    • 0002944001 scopus 로고
    • The space structure near a blow-up point for semilinear heat equations: A formal approach
    • J. J. L. Velázquez, V. A. Galaktionov and M. A. Herrero. The space structure near a blow-up point for semilinear heat equations: a formal approach. Zh. Vychisl. Mat. i Mat. Fiz. 31 (1991), 399-411;
    • (1991) Zh. Vychisl. Mat. I Mat. Fiz. , vol.31 , pp. 399-411
    • Velázquez, J.J.L.1    Galaktionov, V.A.2    Herrero, M.A.3


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