메뉴 건너뛰기




Volumn 5, Issue 4, 1999, Pages 905-928

Unfocused blow up solutions of semilinear parabolic equations

Author keywords

Asymptotic blow up behavior; Blow up radius; Final time profile; Finite time blow up; Semilinear parabolic equation; Unfocused solution

Indexed keywords


EID: 0033412593     PISSN: 10780947     EISSN: None     Source Type: Journal    
DOI: 10.3934/dcds.1999.5.905     Document Type: Article
Times cited : (13)

References (37)
  • 1
    • 0000461055 scopus 로고
    • Remarks on blow-up and non-existence theorems for nonlinear evolution equations
    • J. M. Ball, Remarks on blow-up and non-existence theorems for nonlinear evolution equations, Quart. J. Math. Oxford Ser. (2) 28 (1977), 473-486.
    • (1977) Quart. J. Math. Oxford Ser. (2) , vol.28 , pp. 473-486
    • Ball, J.M.1
  • 2
    • 0030443821 scopus 로고    scopus 로고
    • A nonlinear heat equation with singular initial data
    • H. Brezis, T. Cazenave, A nonlinear heat equation with singular initial data, J. Anal. Math. 68 (1996), 277-304.
    • (1996) J. Anal. Math. , vol.68 , pp. 277-304
    • Brezis, H.1    Cazenave, T.2
  • 3
    • 0013158824 scopus 로고
    • The existence of bounded solutions of a semilinear elliptic equation
    • C. J. Budd, Y.-W. Qi, The existence of bounded solutions of a semilinear elliptic equation, J. Differential Equations 82 (1989), 207-218.
    • (1989) J. Differential Equations , vol.82 , pp. 207-218
    • Budd, C.J.1    Qi, Y.-W.2
  • 4
    • 50849145650 scopus 로고
    • Convergence, asymptotic periodicity and finite point blow-up in one-dimensional semilinear heat equations
    • X. Y. Chen, H. Matano, Convergence, asymptotic periodicity and finite point blow-up in one-dimensional semilinear heat equations, J. Differential Equations 78 (1989), 160-190.
    • (1989) J. Differential Equations , vol.78 , pp. 160-190
    • Chen, X.Y.1    Matano, H.2
  • 5
    • 0007283369 scopus 로고
    • Blow up solutions of a semilinear parabolic equation with the Neumann and Robin boundary conditions
    • Y. G. Chen, Blow up solutions of a semilinear parabolic equation with the Neumann and Robin boundary conditions, J. Fac. Sci. Univ. Tokyo, Sect. IA Math. 37 (1990), 537-574.
    • (1990) J. Fac. Sci. Univ. Tokyo, Sect. IA Math. , vol.37 , pp. 537-574
    • Chen, Y.G.1
  • 7
    • 0001336526 scopus 로고
    • On the blowup of multidimensional semilinear parabolic equations
    • S. Filippas, W. Liu, On the blowup of multidimensional semilinear parabolic equations, Ann. Inst. H. Poincaré Anal. Non Linéaire 10 (1993), 313-344.
    • (1993) Ann. Inst. H. Poincaré Anal. Non Linéaire , vol.10 , pp. 313-344
    • Filippas, S.1    Liu, W.2
  • 9
    • 0000546335 scopus 로고
    • Blow-up of positive solutions of semilinear heat equations
    • A. Friedman, B. McLeod, Blow-up of positive solutions of semilinear heat equations, Indiana Univ. Math. J. 34 (1985), 425-447.
    • (1985) Indiana Univ. Math. J. , vol.34 , pp. 425-447
    • Friedman, A.1    McLeod, B.2
  • 11
    • 0010505120 scopus 로고
    • Application of new comparison theorems in the investigation of unbounded solutions of nonlinear parabolic equations
    • V. A. Galaktionov, S. A. Posaskhov, Application of new comparison theorems in the investigation of unbounded solutions of nonlinear parabolic equations, (in Russian), Differ. Uravn. 22 (1986), 1165-1173. English translation: Differential Equations 22 (1986), 809-815.
    • (1986) Differ. Uravn. , vol.22 , pp. 1165-1173
    • Galaktionov, V.A.1    Posaskhov, S.A.2
  • 12
    • 0001457899 scopus 로고
    • V. A. Galaktionov, S. A. Posaskhov, Application of new comparison theorems in the investigation of unbounded solutions of nonlinear parabolic equations, (in Russian), Differ. Uravn. 22 (1986), 1165-1173. English translation: Differential Equations 22 (1986), 809-815.
    • (1986) Differential Equations , vol.22 , pp. 809-815
  • 13
    • 84988205907 scopus 로고
    • A local characterization of blowup points in semilinear heat equations
    • Y. Giga, A local characterization of blowup points in semilinear heat equations, Lecture Notes Numer. Appl. Anal. 10, 1-14 (1989), Recent Topics in Nonlinear PDE IV, Vol. 160, North Holland, Kyoto, 1988.
    • (1989) Lecture Notes Numer. Appl. Anal. , vol.10 , pp. 1-14
    • Giga, Y.1
  • 14
    • 85034558246 scopus 로고
    • North Holland, Kyoto
    • Y. Giga, A local characterization of blowup points in semilinear heat equations, Lecture Notes Numer. Appl. Anal. 10, 1-14 (1989), Recent Topics in Nonlinear PDE IV, Vol. 160, North Holland, Kyoto, 1988.
    • (1988) Recent Topics in Nonlinear PDE IV , vol.160
  • 15
    • 84990616610 scopus 로고
    • Asymptotically self-similar blow-up of semilinear heat equations
    • Y. Giga, R. 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.2
  • 16
    • 0000332576 scopus 로고
    • Characterizing blowup using similarity variables
    • Y. Giga, R. Kohn, Characterizing blowup 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.2
  • 17
    • 84990575181 scopus 로고
    • Nondegeneracy of blowup for semilinear heat equations
    • Y. Giga, R. 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.2
  • 18
    • 0346153237 scopus 로고
    • Removability of blowup points for semilinear heat equations
    • Dekker
    • Y. Giga, R. Kohn, Removability of blowup points for semilinear heat equations, Lecture Notes in Pure and Appl. Math. 118, Dekker (1989), 257-264.
    • (1989) Lecture Notes in Pure and Appl. Math. , vol.118 , pp. 257-264
    • Giga, Y.1    Kohn, R.2
  • 20
    • 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, No. 5, (1992), 973-997.
    • (1992) Differential Integral Equations , vol.5 , Issue.5 , pp. 973-997
    • Herrero, M.A.1    Velázquez, J.J.L.2
  • 21
    • 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 (182) (1992), 205-219.
    • (1992) Comm. Partial Differential Equations , vol.17 , Issue.182 , pp. 205-219
    • Herrero, M.A.1    Velázquez, J.J.L.2
  • 22
    • 0000172301 scopus 로고
    • Explosion de solutions des équations paraboliques semilinéaires supercritiques
    • M. A. Herrero, J. J. L. Velázquez, Explosion de solutions des équations paraboliques semilinéaires supercritiques, C. R. Acad. Sci. Paris, t. 319 (1994), 141-145.
    • (1994) C. R. Acad. Sci. Paris , vol.319 , pp. 141-145
    • Herrero, M.A.1    Velázquez, J.J.L.2
  • 23
    • 84980080195 scopus 로고
    • On the growth of solutions of quasilinear parabolic equations
    • S. Kaplan, On the growth of solutions of quasilinear parabolic equations, Comm. Pure Appl. Math. 16 (1963), 327-330.
    • (1963) Comm. Pure Appl. Math. , vol.16 , pp. 327-330
    • Kaplan, S.1
  • 24
    • 84948486085 scopus 로고
    • Remarks on the large time behaviour of a nonlinear diffusion equation
    • O. Kavian, Remarks on the large time behaviour of a nonlinear diffusion equation, Ann. Inst. Henri Poincaré Anal. Non Linéaire 4, No. 5 (1987), 423-452.
    • (1987) Ann. Inst. Henri Poincaré Anal. Non Linéaire , vol.4 , Issue.5 , pp. 423-452
    • Kavian, O.1
  • 26
    • 0012859161 scopus 로고
    • Self-similar solutions of a semilinear heat equation
    • in Russian
    • L. A. Lepin, Self-similar solutions of a semilinear heat equation, Math. Modelling, Vol. 2, No. 3 (1990), 63-74 (in Russian).
    • (1990) Math. Modelling , vol.2 , Issue.3 , pp. 63-74
    • Lepin, L.A.1
  • 28
    • 0346783673 scopus 로고    scopus 로고
    • Blow up of critical and subcritical norms in semilinear heat equations
    • J. Matos, Blow up of critical and subcritical norms in semilinear heat equations, Adv. Differential Equations 3, No. 4 (1998), 497-532.
    • (1998) Adv. Differential Equations , vol.3 , Issue.4 , pp. 497-532
    • Matos, J.1
  • 29
    • 0032338170 scopus 로고    scopus 로고
    • Optimal estimates for blow-up rate and behavior for nonlinear heat equations
    • F. Merle, H. Zaag, Optimal estimates for blow-up rate and behavior for nonlinear heat equations, Comm. Pure Appl. Math, Vol. LI (1998), 139-196.
    • (1998) Comm. Pure Appl. Math , vol.51 , pp. 139-196
    • Merle, F.1    Zaag, H.2
  • 30
    • 85034187617 scopus 로고    scopus 로고
    • Refined uniform estimates at blow-up and applications for nonlinear heat equations
    • to appear
    • F. Merle, H. Zaag, Refined uniform estimates at blow-up and applications for nonlinear heat equations, to appear in Geom. Funct. Anal.
    • Geom. Funct. Anal.
    • Merle, F.1    Zaag, H.2
  • 33
    • 38248998988 scopus 로고
    • Local behaviour near blow up points for semilinear parabolic equations
    • J. J. L. Velázquez, Local behaviour near blow up points for semilinear parabolic equations, J. Differential Equations 106, No. 2 (1993), 384-415.
    • (1993) J. Differential Equations , vol.106 , Issue.2 , pp. 384-415
    • Velázquez, J.J.L.1
  • 34
    • 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, No. 1 (1993), 441-464.
    • (1993) Trans. Amer. Math. Soc. , vol.338 , Issue.1 , pp. 441-464
    • Velázquez, J.J.L.1
  • 35
    • 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, No. 9-10 (1992), 1567-1696.
    • (1992) Comm. Partial Differential Equations , vol.17 , Issue.9-10 , pp. 1567-1696
    • Velázquez, J.J.L.1
  • 36
    • 51249183619 scopus 로고
    • Existence and nonexistence of global solutions for a semilinear heat equation
    • F. B. Weissler, Existence and nonexistence of global solutions for a semilinear heat equation, Israel J. Math. 38 (1981), 29-40.
    • (1981) Israel J. Math. , vol.38 , pp. 29-40
    • Weissler, F.B.1
  • 37
    • 0000416165 scopus 로고
    • p-energy and blow-up for a semilinear heat equation
    • p-energy and blow-up for a semilinear heat equation, Proc. Sympos. Pure Math. 45, Part 2 (1986).
    • (1986) Proc. Sympos. Pure Math. , vol.45 , Issue.2 PART
    • Weissler, F.B.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.