메뉴 건너뛰기




Volumn 232, Issue 1, 2007, Pages 176-211

Existence of type II blowup solutions for a semilinear heat equation with critical nonlinearity

Author keywords

Blowup rate; Critical nonlinearity; Self similar solution; Semilinear heat equation; Type II blow up

Indexed keywords


EID: 33750177589     PISSN: 00220396     EISSN: 10902732     Source Type: Journal    
DOI: 10.1016/j.jde.2006.07.012     Document Type: Article
Times cited : (11)

References (29)
  • 1
    • 84942222028 scopus 로고
    • The zero set of a solution of a parabolic equation
    • Angenent S. The zero set of a solution of a parabolic equation. J. Reine Angew. Math. 390 (1988) 79-96
    • (1988) J. Reine Angew. Math. , vol.390 , pp. 79-96
    • Angenent, S.1
  • 3
    • 0001735158 scopus 로고
    • Remarks on the Schrödinger operator with singular complex potentials
    • Brezis H., and Kato T. Remarks on the Schrödinger operator with singular complex potentials. J. Math. Pures Appl. (9) 58 (1979) 137-151
    • (1979) J. Math. Pures Appl. (9) , vol.58 , pp. 137-151
    • Brezis, H.1    Kato, T.2
  • 4
    • 84941275804 scopus 로고
    • A relation between pointwise convergence of functions and convergence of functionals
    • Brezis H., and Lieb E. A relation between pointwise convergence of functions and convergence of functionals. Proc. Amer. Math. Soc. 88 (1983) 486-490
    • (1983) Proc. Amer. Math. Soc. , vol.88 , pp. 486-490
    • Brezis, H.1    Lieb, E.2
  • 5
    • 84990613834 scopus 로고
    • Positive solutions of nonlinear elliptic equations involving critical Sobolev exponents
    • Brezis H., and Nirenberg L. Positive solutions of nonlinear elliptic equations involving critical Sobolev exponents. Comm. Pure Appl. Math. 36 (1983) 437-477
    • (1983) Comm. Pure Appl. Math. , vol.36 , pp. 437-477
    • Brezis, H.1    Nirenberg, L.2
  • 6
    • 84969732524 scopus 로고    scopus 로고
    • Asymptotic periodicity of positive solutions of reaction-diffusion equations on a ball
    • Chen X.-Y., and Polačik P. Asymptotic periodicity of positive solutions of reaction-diffusion equations on a ball. J. Reine Angew. Math. 472 (1996) 17-51
    • (1996) J. Reine Angew. Math. , vol.472 , pp. 17-51
    • Chen, X.-Y.1    Polačik, P.2
  • 7
    • 66049138383 scopus 로고    scopus 로고
    • Blow-up of solutions of supercritical parabolic equations
    • Evolutionary Equations, vol. 2, North-Holland, Amsterdam
    • Fila M. Blow-up of solutions of supercritical parabolic equations. Evolutionary Equations, vol. 2. Handb. Differ. Equ. (2005), North-Holland, Amsterdam 105-158
    • (2005) Handb. Differ. Equ. , pp. 105-158
    • Fila, M.1
  • 8
    • 0011234286 scopus 로고    scopus 로고
    • Fast blow-up mechanisms for sign-changing solutions of a semilinear parabolic equation with critical nonlinearity
    • Filippas S., Herrero M.A., and Velázquez J.J.L. Fast blow-up mechanisms for sign-changing solutions of a semilinear parabolic equation with critical nonlinearity. Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 456 2004 (2000) 2957-2982
    • (2000) Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. , vol.456 , Issue.2004 , pp. 2957-2982
    • Filippas, S.1    Herrero, M.A.2    Velázquez, J.J.L.3
  • 9
    • 0000546335 scopus 로고
    • Blow-up of positive solutions of semilinear heat equations
    • Friedman A., and McLeod B. 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
  • 10
    • 33750183566 scopus 로고    scopus 로고
    • β. Localization, asymptotic behavior of unbounded solutions, preprint, no. 97, Akad. Nauk SSSR, Inst. Prikl. Mat., 1985, 30 pp. (in Russian)
  • 11
    • 0010505120 scopus 로고
    • Application of new comparison theorems to the investigation of unbounded solutions of nonlinear parabolic equations
    • Galaktionov V.A., and Posashkov S.A. Application of new comparison theorems to the investigation of unbounded solutions of nonlinear parabolic equations. Differ. Uravn. 22 (1986) 1165-1173
    • (1986) Differ. Uravn. , vol.22 , pp. 1165-1173
    • Galaktionov, V.A.1    Posashkov, S.A.2
  • 12
    • 0001464964 scopus 로고
    • A bound for global solutions of semilinear heat equations
    • Giga Y. A bound for global solutions of semilinear heat equations. Comm. Math. Phys. 103 (1986) 415-421
    • (1986) Comm. Math. Phys. , vol.103 , pp. 415-421
    • Giga, Y.1
  • 13
    • 84990616610 scopus 로고
    • Asymptotically self-similar blowup of semilinear heat equations
    • Giga Y., and Kohn R.V. Asymptotically 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
  • 14
    • 0000332576 scopus 로고
    • Characterizing blowup using similarity variables
    • Giga Y., and Kohn R. 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
  • 15
    • 84990575181 scopus 로고
    • Nondegeneracy of blowup for semilinear heat equations
    • Giga Y., and Kohn R. 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.2
  • 16
    • 3042688935 scopus 로고    scopus 로고
    • Blow-up rate for semilinear heat equations with subcritical nonlinearity
    • Giga Y., Matsui S., and Sasayama S. Blow-up rate for semilinear heat equations with subcritical nonlinearity. Indiana Univ. Math. J. 53 (2004) 483-514
    • (2004) Indiana Univ. Math. J. , vol.53 , pp. 483-514
    • Giga, Y.1    Matsui, S.2    Sasayama, S.3
  • 17
    • 4744344778 scopus 로고    scopus 로고
    • On blow-up rate for sign-changing solutions in a convex domain
    • Giga Y., Matsui S., and Sasayama S. On blow-up rate for sign-changing solutions in a convex domain. Math. Methods Appl. Sci. 27 (2004) 1771-1782
    • (2004) Math. Methods Appl. Sci. , vol.27 , pp. 1771-1782
    • Giga, Y.1    Matsui, S.2    Sasayama, S.3
  • 19
    • 0000172301 scopus 로고
    • Explosion de solutions d'équations paraboliques semilinéaires supercritiques
    • Herrero M.A., and Velázquez J.J.L. Explosion de solutions d'équations paraboliques semilinéaires supercritiques. C. R. Acad. Sci. Paris Sér. I Math. 319 (1994) 141-145
    • (1994) C. R. Acad. Sci. Paris Sér. I Math. , vol.319 , pp. 141-145
    • Herrero, M.A.1    Velázquez, J.J.L.2
  • 20
    • 33750172330 scopus 로고    scopus 로고
    • M.A. Herrero, J.J.L. Velázquez, A blow-up result for semilinear heat equations in the supercritical case, preprint
  • 21
    • 1642534230 scopus 로고    scopus 로고
    • Semilinear parabolic equations involving critical Sobolev exponent: Local and asymptotic behavior of solutions
    • Ikehata R., and Suzuki T. Semilinear parabolic equations involving critical Sobolev exponent: Local and asymptotic behavior of solutions. Differential Integral Equations 13 (2000) 869-901
    • (2000) Differential Integral Equations , vol.13 , pp. 869-901
    • Ikehata, R.1    Suzuki, T.2
  • 22
    • 0003223550 scopus 로고    scopus 로고
    • Linear and Quasilinear Equations of Parabolic Type
    • Amer. Math. Soc., Providence, RI
    • Ladyženskaja O.A., Solonnikov V.A., and Ural'ceva N.N. Linear and Quasilinear Equations of Parabolic Type. Transl. Math. Monogr. vol. 23 (1996), Amer. Math. Soc., Providence, RI
    • (1996) Transl. Math. Monogr. , vol.23
    • Ladyženskaja, O.A.1    Solonnikov, V.A.2    Ural'ceva, N.N.3
  • 23
    • 0000657925 scopus 로고
    • Nonincrease of the lap-number of a solution for a one-dimensional semilinear parabolic equation
    • Matano H. Nonincrease of the lap-number of a solution for a one-dimensional semilinear parabolic equation. J. Fac. Sci. Univ. Tokyo Sect. IA Math. 29 (1982) 401-441
    • (1982) J. Fac. Sci. Univ. Tokyo Sect. IA Math. , vol.29 , pp. 401-441
    • Matano, H.1
  • 24
    • 7044224827 scopus 로고    scopus 로고
    • On nonexistence of type II blowup for a supercritical nonlinear heat equation
    • Matano H., and Merle F. On nonexistence of type II blowup for a supercritical nonlinear heat equation. Comm. Pure Appl. Math. 57 (2004) 1494-1541
    • (2004) Comm. Pure Appl. Math. , vol.57 , pp. 1494-1541
    • Matano, H.1    Merle, F.2
  • 25
    • 59849107682 scopus 로고    scopus 로고
    • Type-II blowup for a semilinear heat equation
    • Mizoguchi N. Type-II blowup for a semilinear heat equation. Adv. Differential Equations 9 (2004) 1279-1316
    • (2004) Adv. Differential Equations , vol.9 , pp. 1279-1316
    • Mizoguchi, N.1
  • 26
    • 4344718737 scopus 로고    scopus 로고
    • Blowup behavior of solutions for a semilinear heat equation with supercritical nonlinearity
    • Mizoguchi N. Blowup behavior of solutions for a semilinear heat equation with supercritical nonlinearity. J. Differential Equations 205 (2004) 298-328
    • (2004) J. Differential Equations , vol.205 , pp. 298-328
    • Mizoguchi, N.1
  • 27
    • 0003187917 scopus 로고
    • Single point blow-up for a general semilinear heat equation
    • Mueller C.E., and Weissler F.B. Single point blow-up for a general semilinear heat equation. Indiana Univ. Math. J. 34 (1985) 881-913
    • (1985) Indiana Univ. Math. J. , vol.34 , pp. 881-913
    • Mueller, C.E.1    Weissler, F.B.2
  • 28
    • 0001755361 scopus 로고
    • A nonlinear Dirichlet problem on the unit ball and its applications
    • Ni W.-M. A nonlinear Dirichlet problem on the unit ball and its applications. Indiana Univ. Math. J. 31 (1982) 801-807
    • (1982) Indiana Univ. Math. J. , vol.31 , pp. 801-807
    • Ni, W.-M.1
  • 29
    • 84968512169 scopus 로고
    • On the Cauchy problem for reaction-diffusion equations
    • Wang X. On the Cauchy problem for reaction-diffusion equations. Trans. Amer. Math. Soc. 337 (1993) 549-590
    • (1993) Trans. Amer. Math. Soc. , vol.337 , pp. 549-590
    • Wang, X.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.