메뉴 건너뛰기




Volumn 15, Issue 5, 1998, Pages 581-622

Blow-up results for vector-valued nonlinear heat equations with no gradient structure

Author keywords

35B40: asymptotic behavior of solutions; 35K: parabolic systems

Indexed keywords


EID: 0000201979     PISSN: 02941449     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0294-1449(98)80002-4     Document Type: Article
Times cited : (61)

References (20)
  • 1
    • 0000461055 scopus 로고
    • Remarks on blow-up and nonexistence theorems for nonlinear evolution equations
    • J. BALL, Remarks on blow-up and nonexistence theorems for nonlinear evolution equations, Quart. J. Math. Oxford, Vol. 28, 1977, pp. 473-486.
    • (1977) Quart. J. Math. Oxford , vol.28 , pp. 473-486
    • Ball, J.1
  • 2
    • 84990610650 scopus 로고
    • A rescaling algorithm for the numerical calculation of blowing-up solutions
    • M. BERGER and R. KOHN, A rescaling algorithm for the numerical calculation of blowing-up solutions, Comm. Pure Appl. Math., Vol. 41, 1988, pp. 841-863.
    • (1988) Comm. Pure Appl. Math. , vol.41 , pp. 841-863
    • Berger, M.1    Kohn, R.2
  • 4
    • 0000877190 scopus 로고
    • Universality in blow-up for nonlinear heat equations
    • J. BRICMONT and A. KUPIAINEN, Universality in blow-up for nonlinear heat equations, Nonlinearity, 7, 1994, pp. 539-575.
    • (1994) Nonlinearity , vol.7 , pp. 539-575
    • Bricmont, J.1    Kupiainen, A.2
  • 6
    • 0007452217 scopus 로고
    • Modulation theory for the blowup of vector-valued nonlinear heat equations
    • S. FILIPPAS and F. MERLE, Modulation theory for the blowup of vector-valued nonlinear heat equations, J. Diff. Equations, Vol. 116, 1995, pp. 119-148.
    • (1995) J. Diff. Equations , vol.116 , pp. 119-148
    • Filippas, S.1    Merle, F.2
  • 7
    • 0011609560 scopus 로고
    • On approximate self-similar solutions for some class of quasilinear heat equations with sources
    • V. A. GALAKTIONOV, S. P. KURDYUMOV and A. A. SAMARSKII, On approximate self-similar solutions for some class of quasilinear heat equations with sources, Math. USSR-Sb, Vol. 52, 1985, pp. 155-180.
    • (1985) Math. USSR-Sb , vol.52 , pp. 155-180
    • Galaktionov, V.A.1    Kurdyumov, S.P.2    Samarskii, A.A.3
  • 8
    • 0004528391 scopus 로고
    • Regional blow-up in a semilinear heat equation with convergence to a Hamilton-Jacobi equation
    • V. A. GALAKTIONOV and J. L. VAZQUEZ, Regional blow-up in a semilinear heat equation with convergence to a Hamilton-Jacobi equation, SIAM J. Math. Anal., Vol. 24, 1993, pp. 1254-1276.
    • (1993) SIAM J. Math. Anal. , vol.24 , pp. 1254-1276
    • Galaktionov, V.A.1    Vazquez, J.L.2
  • 9
    • 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., Vol. 38, 1985, pp. 297-319.
    • (1985) Comm. Pure Appl. Math. , vol.38 , pp. 297-319
    • Giga, Y.1    Kohn, R.2
  • 10
    • 0000332576 scopus 로고
    • Characterizing blowup using similarity variables
    • Y. GIGA and R. KOHN, Characterizing blowup using similarity variables, Indiana Univ. Math. J., Vol. 36, 1987, pp. 1-40.
    • (1987) Indiana Univ. Math. J. , vol.36 , pp. 1-40
    • Giga, Y.1    Kohn, R.2
  • 11
    • 84990575181 scopus 로고
    • Nondegeneracy of blow-up for semilinear heat equations
    • Y. GIGA and R. KOHN, Nondegeneracy of blow-up for semilinear heat equations, Comm. Pure Appl. Math., Vol. 42, 1989, pp. 845-884.
    • (1989) Comm. Pure Appl. Math. , vol.42 , pp. 845-884
    • Giga, Y.1    Kohn, R.2
  • 13
    • 85011578583 scopus 로고
    • Blow-up behavior of one-dimensional semilinear parabolic equations
    • M. A. HERRERO and J. J. L. VELAZQUEZ, Blow-up behavior of one-dimensional semilinear parabolic equations, Ann. Inst. Henri Poin- caré, Vol. 10, 1993, pp. 133-189.
    • (1993) Ann. Inst. Henri Poin- Caré , vol.10 , pp. 133-189
    • Herrero, M.A.1    Velazquez, J.J.L.2
  • 14
    • 84972492804 scopus 로고
    • Flat blow-up in one-dimensional semilinear heat equations
    • M. A. HERRERO and J. J. L. VELAZQUEZ, Flat blow-up in one-dimensional semilinear heat equations, Differential and Integral eqns., Vol. 5, 1992, pp. 973-997.
    • (1992) Differential and Integral Eqns. , vol.5 , pp. 973-997
    • Herrero, M.A.1    Velazquez, J.J.L.2
  • 15
    • 0000781993 scopus 로고    scopus 로고
    • The complex Ginzburg-Landau equation as a model problem, Dynamical systems and probabilistic methods in partial differential equations (Berkeley, 1994)
    • Providence, RI
    • C. D. LEVERMORE and M. OLIVER, The complex Ginzburg-Landau equation as a model problem, Dynamical systems and probabilistic methods in partial differential equations (Berkeley, 1994), Lectures in Appl. Math., Vol. 31, Amer. Math. Soc., Providence, RI, 1996, pp. 141-190.
    • (1996) Lectures in Appl. Math., Vol. 31, Amer. Math. Soc. , vol.31 , pp. 141-190
    • Levermore, C.D.1    Oliver, M.2
  • 17
    • 84990556280 scopus 로고
    • Solution of a nonlinear heat equation with arbitrary given blow-up points
    • F. MERLE, Solution of a nonlinear heat equation with arbitrary given blow-up points. Comm. Pure Appl. Math., Vol. 45, 1992, pp. 263-300.
    • (1992) Comm. Pure Appl. Math. , vol.45 , pp. 263-300
    • Merle, F.1
  • 19
    • 84968503478 scopus 로고
    • Classification of singularities for blowing up solutions in higher dimensions
    • J. J. L. VELAZQUEZ, Classification of singularities for blowing up solutions in higher dimensions, Trans. Amer. Math. Soc., Vol. 338, 1993, pp. 441-464.
    • (1993) Trans. Amer. Math. Soc. , vol.338 , pp. 441-464
    • Velazquez, J.J.L.1
  • 20
    • 48549114032 scopus 로고
    • Single-point blowup for a semilinear initial value problem
    • F. WEISSLER, Single-point blowup for a semilinear initial value problem, J. Diff. Equations, Vol. 55, 1984, pp. 204-224.
    • (1984) J. Diff. Equations , vol.55 , pp. 204-224
    • Weissler, F.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.