메뉴 건너뛰기




Volumn 8, Issue 2, 2002, Pages 435-450

O.D.E. type behavior of blow-up solutions of nonlinear heat equations

Author keywords

Blow up; Heat equations; Liouville theorem

Indexed keywords


EID: 23044534732     PISSN: 10780947     EISSN: None     Source Type: Journal    
DOI: 10.3934/dcds.2002.8.435     Document Type: Article
Times cited : (16)

References (25)
  • 1
    • 0000461055 scopus 로고
    • Remarks on blow-up and nonexistence theorems for nonlinear evolution equations
    • J. M. Ball, Remarks on blow-up and nonexistence theorems for nonlinear evolution equations. Quart. J. Math. Oxford Ser. (2) 28(112) (1977), 473-486.
    • (1977) Quart. J. Math. Oxford Ser. (2) , vol.28 , Issue.112 , pp. 473-486
    • Ball, J.M.1
  • 2
    • 0000877190 scopus 로고
    • Universality in blow-up for nonlinear heat equations
    • J. Bricmont, A. Kupiainen, Universality in blow-up for nonlinear heat equations. Nonlinearity 7(2) (1994), 539-575.
    • (1994) Nonlinearity , vol.7 , Issue.2 , pp. 539-575
    • Bricmont, J.1    Kupiainen, A.2
  • 3
    • 0002156334 scopus 로고    scopus 로고
    • Stability of the blow-up profile of non-linear heat equations from the dynamical system point of view
    • C. Fermanian Kammerer, F. Merle, H. Zaag, Stability of the blow-up profile of non-linear heat equations from the dynamical system point of view. Math. Ann. 317(2) (2000), 347-387.
    • (2000) Math. Ann. , vol.317 , Issue.2 , pp. 347-387
    • Kammerer, C.F.1    Merle, F.2    Zaag, H.3
  • 5
    • 0001336526 scopus 로고
    • On the blowup of multidimensional semilinear heat equations
    • S. Filippas, W. X. Liu, On the blowup of multidimensional semilinear heat equations. Ann. Inst. H. Poincaré Anal. Non Linéaire 10(3) (1993), 313-344.
    • (1993) Ann. Inst. H. Poincaré Anal. Non Linéaire , vol.10 , Issue.3 , pp. 313-344
    • Filippas, S.1    Liu, W.X.2
  • 6
    • 0007452217 scopus 로고
    • Modulation theory for the blowup of vector-valued nonlinear heat equations
    • S. Filippas, F. Merle, Modulation theory for the blowup of vector-valued nonlinear heat equations. J. Differential Equations 116(1) (1995), 119-148.
    • (1995) J. Differential Equations , vol.116 , Issue.1 , pp. 119-148
    • Filippas, S.1    Merle, F.2
  • 7
    • 0040953629 scopus 로고
    • Remarks on nonlinear parabolic equations
    • Amer. Math. Soc., Providence, R.I.
    • A. Friedman, Remarks on nonlinear parabolic equations, Proc. Sympos. Appl. Math., vol. XVII, pp. 3-23, Amer. Math. Soc., Providence, R.I., 1965.
    • (1965) Proc. Sympos. Appl. Math. , vol.17 , pp. 3-23
    • Friedman, A.1
  • 9
    • 84990616610 scopus 로고
    • Asymptotically self-similar blow-up of semilinear heat equations
    • Y. Giga, R. V. Kohn, Asymptotically self-similar blow-up of semilinear heat equations. Comm. Pure Appl. Math. 38(3) (1985), 297-319.
    • (1985) Comm. Pure Appl. Math. , vol.38 , Issue.3 , pp. 297-319
    • Giga, Y.1    Kohn, R.V.2
  • 10
    • 0000332576 scopus 로고
    • Characterizing blowup using similarity variables
    • Y. Giga, R. V. Kohn, Characterizing blowup using similarity variables. Indiana Univ. Math. J. 36(1) (1987), 1-40.
    • (1987) Indiana Univ. Math. J. , vol.36 , Issue.1 , pp. 1-40
    • Giga, Y.1    Kohn, R.V.2
  • 11
    • 84990575181 scopus 로고
    • Nondegeneracy of blowup for semilinear heat equations
    • Y. Giga, R. V. Kohn, Nondegeneracy of blowup for semilinear heat equations. Comm. Pure Appl. Math. 42(6) (1989), 845-884.
    • (1989) Comm. Pure Appl. Math. , vol.42 , Issue.6 , pp. 845-884
    • Giga, Y.1    Kohn, R.V.2
  • 12
    • 0000066418 scopus 로고
    • Blow-up profiles in one-dimensional, semilinear parabolic problems
    • M. A. Herrero, J. J. L. Velázquez, Blow-up profiles in one-dimensional, semilinear parabolic problems. Comm. Partial Differential Equations 17(1-2) (1992), 205-219.
    • (1992) Comm. Partial Differential Equations , vol.17 , Issue.1-2 , pp. 205-219
    • Herrero, M.A.1    Velázquez, J.J.L.2
  • 13
    • 84972492804 scopus 로고
    • Flat blow-up in one-dimensional semilinear heat equations
    • M. A. Herrero, J. J. L. Velázquez, Flat blow-up in one-dimensional semilinear heat equations. Differential Integral Equations 5(5) (1992), 973-997.
    • (1992) Differential Integral Equations , vol.5 , Issue.5 , pp. 973-997
    • Herrero, M.A.1    Velázquez, J.J.L.2
  • 16
    • 84990556280 scopus 로고
    • Solution of a nonlinear heat equation with arbitrarily given blow-up points
    • F. Merle, Solution of a nonlinear heat equation with arbitrarily given blow-up points. Comm. Pure Appl. Math. 45(3) (1992), 263-300.
    • (1992) Comm. Pure Appl. Math. , vol.45 , Issue.3 , pp. 263-300
    • Merle, F.1
  • 17
    • 0034407299 scopus 로고    scopus 로고
    • A Liouville theorem for vector-valued nonlinear heat equations and applications
    • F. Merle, H. Zaag, A Liouville theorem for vector-valued nonlinear heat equations and applications. Math. Ann. 316(1) (2000), 103-137.
    • (2000) Math. Ann. , vol.316 , Issue.1 , pp. 103-137
    • Merle, F.1    Zaag, H.2
  • 19
    • 0032338170 scopus 로고    scopus 로고
    • Optimal estimates for blowup rate and behavior for nonlinear heat equations
    • F. Merle, H. Zaag, Optimal Estimates for Blowup Rate and Behavior for Nonlinear Heat Equations. Comm. Pure Appl. Math. 51(2) (1998), 139-196.
    • (1998) Comm. Pure Appl. Math. , vol.51 , Issue.2 , pp. 139-196
    • Merle, F.1    Zaag, H.2
  • 20
    • 0032218494 scopus 로고    scopus 로고
    • Refined uniform estimates at blow-up and applications for nonlinear heat equations
    • F. Merle, H. Zaag, Refined uniform estimates at blow-up and applications for nonlinear heat equations. Geom. Funct. Anal. 8(6) (1998), 1043-1085.
    • (1998) Geom. Funct. Anal. , vol.8 , Issue.6 , pp. 1043-1085
    • Merle, F.1    Zaag, H.2
  • 21
    • 0000428167 scopus 로고
    • Higher-dimensional blow up for semilinear parabolic equations
    • J. J. L. Velázquez, Higher-dimensional blow up for semilinear parabolic equations. Comm. Partial Differential Equations 17(9-10) (1992), 1567-1596.
    • (1992) Comm. Partial Differential Equations , vol.17 , Issue.9-10 , pp. 1567-1596
    • Velázquez, J.J.L.1
  • 22
    • 84968503478 scopus 로고
    • Classification of singularities for blowing up solutions in higher dimensions
    • J. J. L. Velázquez, Classification of singularities for blowing up solutions in higher dimensions. Trans. Amer. Math. Soc. 338(1) (1993), 441-464.
    • (1993) Trans. Amer. Math. Soc. , vol.338 , Issue.1 , pp. 441-464
    • Velázquez, J.J.L.1
  • 23
    • 0001494169 scopus 로고
    • Estimates on the (n - 1)-dimensional Hausdorff measure of the blow-up set for a semilinear heat equation
    • J. J. L. Velázquez, Estimates on the (n - 1)-dimensional Hausdorff measure of the blow-up set for a semilinear heat equation. Indiana Univ. Math. J. 42(2) (1993), 445-176.
    • (1993) Indiana Univ. Math. J. , vol.42 , Issue.2 , pp. 445-1176
    • Velázquez, J.J.L.1
  • 24
    • 0035526708 scopus 로고    scopus 로고
    • A Liouville theorem and blow-up behavior for a vector-valued nonlinear heat equation with no gradient structure
    • H. Zaag, A Liouville theorem and blow-up behavior for a vector-valued nonlinear heat equation with no gradient structure. Comm. Pure Appl. Math. 54 (2001), 107-133.
    • (2001) Comm. Pure Appl. Math. , vol.54 , pp. 107-133
    • Zaag, H.1
  • 25
    • 0000201979 scopus 로고    scopus 로고
    • Blow-up results for vector-valued nonlinear heat equations with no gradient structure
    • H. Zaag, Blow-up results for vector-valued nonlinear heat equations with no gradient structure. Ann. Inst. H. Poincaré Anal. Non Linéaire 15(5) (1998), 581-622.
    • (1998) Ann. Inst. H. Poincaré Anal. Non Linéaire , vol.15 , Issue.5 , pp. 581-622
    • Zaag, H.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.