메뉴 건너뛰기




Volumn 50, Issue 3, 1999, Pages 361-374

The blow-up properties of solutions to semilinear heat equations with nonlinear boundary conditions

Author keywords

Blow up point; Blow up rate; Nonlinear boundary conditions; Semilinear heat equation

Indexed keywords


EID: 0033245819     PISSN: 00442275     EISSN: None     Source Type: Journal    
DOI: 10.1007/s000330050023     Document Type: Article
Times cited : (34)

References (18)
  • 1
    • 0001676026 scopus 로고
    • The blow-up behavior of the heat equation with Neumann boundary conditions
    • Keng Deng, The blow-up behavior of the heat equation with Neumann boundary conditions, J. Math. Anal., and Appl. 188 (1994), 645-650.
    • (1994) J. Math. Anal., and Appl. , vol.188 , pp. 645-650
    • Deng, K.1
  • 2
    • 84988159342 scopus 로고
    • The blow up rate for the heat equation with a nonlinear boundary condition
    • M. Fila and P. Quittner, The blow up rate for the heat equation with a nonlinear boundary condition, Math. Methods Appl. Sci. 14 (1991), 197-205.
    • (1991) Math. Methods Appl. Sci. , vol.14 , pp. 197-205
    • Fila, M.1    Quittner, P.2
  • 3
    • 38249010341 scopus 로고
    • Diffusivity versus absorption through the boundary
    • J. Filo, Diffusivity versus absorption through the boundary, J. Differential Equations 99 (1992), 281-305.
    • (1992) J. Differential Equations , vol.99 , pp. 281-305
    • Filo, J.1
  • 5
    • 0000546335 scopus 로고
    • Blowup of positive solutions of semilinear heat equations
    • A. Friedman and B. Mcleod, Blowup of positive solutions of semilinear heat equations, Indiana Univ. Math. J. 34 (1985), 425-477.
    • (1985) Indiana Univ. Math. J. , vol.34 , pp. 425-477
    • Friedman, A.1    Mcleod, B.2
  • 6
    • 84980182383 scopus 로고
    • Global and local behavior of positive solutions of nonlinear elliptic equations
    • B. Gidas and J. Spruck, Global and local behavior of positive solutions of nonlinear elliptic equations, Comm. Pure Appl. Math. 34 (1981), 525-598.
    • (1981) Comm. Pure Appl. Math. , vol.34 , pp. 525-598
    • Gidas, B.1    Spruck, J.2
  • 7
    • 84939873114 scopus 로고
    • A prior bounds for positive solutions of nonlinear elliptic equations
    • B. Gidas and J. Spruck, A prior bounds for positive solutions of nonlinear elliptic equations, Comm. Partial Diff. Eq. 8 (1981), 883-901.
    • (1981) Comm. Partial Diff. Eq. , vol.8 , pp. 883-901
    • Gidas, B.1    Spruck, J.2
  • 8
    • 84990616610 scopus 로고
    • Asymptotic self-similar blowup of semilinear heat equations
    • Y. Giga and R. V. Kohn, Asymptotic self-similar blowup 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
  • 9
    • 0000332576 scopus 로고
    • Characterizing blowup using similarity variables
    • Y. Giga and R. V. Kohn, Characterizing blowup using similarity variables, Indiana Univ. Math. J. 36 (L987), 425-447.
    • (1987) Indiana Univ. Math. J. , vol.36 , pp. 425-447
    • Giga, Y.1    Kohn, R.V.2
  • 10
    • 84990575181 scopus 로고
    • Nondegeneracy of blowup for semilinear heat equations
    • Y. Giga and R. V. Kohn, Nondegeneracy of blowup for semilinear heat equations, Comm. Pure Appl. Math. 42 (1989), 845-884.
    • (1989) Comm. Pure Appl. Math. , vol.42 , pp. 845-884
    • Giga, Y.1    Kohn, R.V.2
  • 11
    • 0001664892 scopus 로고
    • Blow up results and localization of blow up points for the heat equation with a nonlinear boundary condition
    • J. L. Gomez, V. Marquez and N. Wolanski, Blow up results and localization of blow up points for the heat equation with a nonlinear boundary condition, J. Diff. Eq. 92 (1991), 384-401.
    • (1991) J. Diff. Eq. , vol.92 , pp. 384-401
    • Gomez, J.L.1    Marquez, V.2    Wolanski, N.3
  • 12
    • 0001075681 scopus 로고
    • Nondegeneracy and single-point-blowup for solution of the heat equation with a nonlinear boundary condition
    • Bei Hu, Nondegeneracy and single-point-blowup for solution of the heat equation with a nonlinear boundary condition, J. Math. Sci. Univ. Tokyo 1 (1994), 251-276.
    • (1994) J. Math. Sci. Univ. Tokyo , vol.1 , pp. 251-276
    • Hu, B.1
  • 13
    • 84968468748 scopus 로고
    • The profile near blowup time for solutions of the heat equation with a nonlinear boundary condition
    • Bei Hu and H. M. Yin, The profile near blowup time for solutions of the heat equation with a nonlinear boundary condition, Transactions Amer. Soc. 346 (1994), 117-135.
    • (1994) Transactions Amer. Soc. , vol.346 , pp. 117-135
    • Hu, B.1    Yin, H.M.2
  • 15
    • 0023212981 scopus 로고
    • A potential well theory for the heat equation with a nonlinear boundary condition
    • H. A. Levine and R. A. Smith, A potential well theory for the heat equation with a nonlinear boundary condition, Math. Methods Appl. Sci. 9 (1987), 127-136.
    • (1987) Math. Methods Appl. Sci. , vol.9 , pp. 127-136
    • Levine, H.A.1    Smith, R.A.2
  • 16
    • 0000058950 scopus 로고
    • The blow-up rate of solutions of semilinear heat equations
    • Wenxiong Liu, The blow-up rate of solutions of semilinear heat equations, J. of Diff. Eq. 77 (1989), 104-122.
    • (1989) J. of Diff. Eq. , vol.77 , pp. 104-122
    • Liu, W.1
  • 17
    • 0003088926 scopus 로고
    • On existence and nonexistence in the large of solutions of parabolic differential equations with a nonlinear boundary condition
    • W. Walter, On existence and nonexistence in the large of solutions of parabolic differential equations with a nonlinear boundary condition, SIAM J. Math. Anal. 6 (1975), 85-90.
    • (1975) SIAM J. Math. Anal. , vol.6 , pp. 85-90
    • Walter, W.1
  • 18
    • 84990581880 scopus 로고
    • ∞ blow-up estimate for nonlinear heat equation
    • ∞ blow-up estimate for nonlinear heat equation, Comm. Pure Appl. Math. 38 (1985), 291-295.
    • (1985) Comm. Pure Appl. Math. , vol.38 , pp. 291-295
    • Weissler, F.B.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.