메뉴 건너뛰기




Volumn 17, Issue 3, 2004, Pages 1075-1099

On very singular similarity solutions of a higher-order semilinear parabolic equation

Author keywords

[No Author keywords available]

Indexed keywords


EID: 2442650474     PISSN: 09517715     EISSN: None     Source Type: Journal    
DOI: 10.1088/0951-7715/17/3/017     Document Type: Article
Times cited : (30)

References (43)
  • 1
    • 0000329412 scopus 로고
    • The Morse-Smale property for a semi-linear parabolic equation
    • Angenent S B 1986 The Morse-Smale property for a semi-linear parabolic equation J. Diff. Eqns 62 427-42
    • (1986) J. Diff. Eqns. , vol.62 , pp. 427-442
    • Angenent, S.B.1
  • 2
    • 0032368532 scopus 로고    scopus 로고
    • Long-wave instabilities and saturation in thin film equations
    • Bertozzi A L and Pugh M C 1998 Long-wave instabilities and saturation in thin film equations Commun. Pure Appl. Math. LI 625-51
    • (1998) Commun. Pure Appl. Math. , vol.51 , pp. 625-651
    • Bertozzi, A.L.1    Pugh, M.C.2
  • 3
    • 2442638579 scopus 로고    scopus 로고
    • Self-similar blow-up in higher-order semilinear parabolic equations
    • at press
    • Budd C J, Galaktionov V A and Williams J F 2004 Self-similar blow-up in higher-order semilinear parabolic equations SIAM J. Appl. Math. at press, http://www.maths.bath.ac.uk/MATHEMATICS/preprints.html
    • (2004) SIAM J. Appl. Math.
    • Budd, C.J.1    Galaktionov, V.A.2    Williams, J.F.3
  • 5
    • 0002538991 scopus 로고
    • Nonlinear parabolic equations involving measures as initial conditions
    • Brezis H and Friedman A 1983 Nonlinear parabolic equations involving measures as initial conditions J. Math. Pure Appl. 62 73-97
    • (1983) J. Math. Pure Appl. , vol.62 , pp. 73-97
    • Brezis, H.1    Friedman, A.2
  • 6
    • 34250123028 scopus 로고
    • A very singular solution of the heat equation with absorption
    • Brezis H, Peletier L A and Terman D 1986 A very singular solution of the heat equation with absorption Arch. Ration. Mech. Anal. 95 185-209
    • (1986) Arch. Ration. Mech. Anal. , vol.95 , pp. 185-209
    • Brezis, H.1    Peletier, L.A.2    Terman, D.3
  • 8
    • 84990739185 scopus 로고
    • Renormalization-group and asymptotics of solutions of nonlinear parabolic equations
    • Bricmont J, Kupiainen A and Lin G 1994 Renormalization-group and asymptotics of solutions of nonlinear parabolic equations Commun. Pure Appl. Math. 47 893-922
    • (1994) Commun. Pure Appl. Math. , vol.47 , pp. 893-922
    • Bricmont, J.1    Kupiainen, A.2    Lin, G.3
  • 10
    • 0003254098 scopus 로고
    • Stability of solutions of differential equations in banach space
    • Providence, RI: American Mathematical Society
    • Daleckii Ju L and Krein M G 1974 Stability of solutions of differential equations in banach space Transl. Math. Monogr. vol 43 (Providence, RI: American Mathematical Society)
    • (1974) Transl. Math. Monogr. , vol.43
    • Daleckii, Ju.L.1    Krein, M.G.2
  • 12
    • 0003487030 scopus 로고    scopus 로고
    • AUTO97: Continuation and bifurcation software for ordinary differential equations
    • Department of Computer Science, Concordia University, Montreal, Canada
    • Doedel E J, Champneys A R, Fairgrieve T F, Kuznetsov Y A, Sandstede B and Wang X-J 1997 AUTO97: Continuation and bifurcation software for ordinary differential equations Technical Report Department of Computer Science, Concordia University, Montreal, Canada, available at ftp://ftp.cs.concordia.ca/ pub/doedel/auto
    • (1997) Technical Report
    • Doedel, E.J.1    Champneys, A.R.2    Fairgrieve, T.F.3    Kuznetsov, Y.A.4    Sandstede, B.5    Wang, X.-J.6
  • 13
    • 0037715273 scopus 로고    scopus 로고
    • Asymptotic behaviour of global solutions to higher-order semilinear parabolic equations in the supercritical range
    • Egorov Yu V, Galaktionov V A, Kondratiev V A and Pohozaev S I 2002 Asymptotic behaviour of global solutions to higher-order semilinear parabolic equations in the supercritical range C. R. Acad. Sci. Paris 335 805-10, http://www.maths.bath.ac.uk/MATHEMATICS/preprints.html
    • (2002) C. R. Acad. Sci. Paris , vol.335 , pp. 805-810
    • Egorov Yu.V1    Galaktionov, V.A.2    Kondratiev, V.A.3    Pohozaev, S.I.4
  • 15
    • 0002436479 scopus 로고
    • Eigenvalue problems for the equation Ly + λp(x)y = 0
    • Ellias U 1978 Eigenvalue problems for the equation Ly + λp(x)y = 0 J. Diff. Eqns 29 28-57
    • (1978) J. Diff. Eqns , vol.29 , pp. 28-57
    • Ellias, U.1
  • 17
    • 0000457881 scopus 로고
    • Variational problems related to self-similar solutions of the heat equation
    • Escobedo M and Kavian O 1987 Variational problems related to self-similar solutions of the heat equation Nonlinear Anal. TMA 11 1103-33
    • (1987) Nonlinear Anal. TMA , vol.11 , pp. 1103-1133
    • Escobedo, M.1    Kavian, O.2
  • 18
    • 2442642353 scopus 로고    scopus 로고
    • Blow-up and global asymptotics of the unstable Cahn-Hilliard equation with a homogeneous nonlinearity
    • submitted
    • Evans J D, Galaktionov V A and Williams J F 2004 Blow-up and global asymptotics of the unstable Cahn-Hilliard equation with a homogeneous nonlinearity SIAM J. Appl. Math. submitted, http://www.maths.bath.ac.uk/ MATHEMATICS/preprints.html
    • (2004) SIAM J. Appl. Math.
    • Evans, J.D.1    Galaktionov, V.A.2    Williams, J.F.3
  • 19
    • 84957170528 scopus 로고
    • Singularities of the kernels of Fourier integral operators and the asymptotic behaviour of the solution of the mixed problem
    • Fedoryuk M V 1977 Singularities of the kernels of Fourier integral operators and the asymptotic behaviour of the solution of the mixed problem Russ. Math. Surveys 32 67-120
    • (1977) Russ. Math. Surveys , vol.32 , pp. 67-120
    • Fedoryuk, M.V.1
  • 21
    • 57249088473 scopus 로고    scopus 로고
    • On a spectrum of blow-up patterns for a higher-order semilinear parabolic equations
    • Galaktionov V A 2001 On a spectrum of blow-up patterns for a higher-order semilinear parabolic equations Proc. R. Soc. A 457 1-21
    • (2001) Proc. R. Soc. A , vol.457 , pp. 1-21
    • Galaktionov, V.A.1
  • 22
    • 2442713535 scopus 로고    scopus 로고
    • Critical global asymptotics in higher-order semilinear parabolic equations
    • Galaktionov V A 2003 Critical global asymptotics in higher-order semilinear parabolic equations Int. J. Math. Math. Sci. 60 3809-25, http://www.maths.bath.ac.uk/MATHEMATICS/preprints.html
    • (2003) Int. J. Math. Math. Sci. , vol.60 , pp. 3809-3825
    • Galaktionov, V.A.1
  • 23
    • 84871172226 scopus 로고
    • On asymptotic 'eigenfunctions' of the Cauchy problem for a nonlinear parabolic equation
    • Galaktionov V A, Kurdyumov S P and Samarskii A A 1986 On asymptotic 'eigenfunctions' of the Cauchy problem for a nonlinear parabolic equation Math. USSR Sbornik 54 421-55
    • (1986) Math. USSR Sbornik , vol.54 , pp. 421-455
    • Galaktionov, V.A.1    Kurdyumov, S.P.2    Samarskii, A.A.3
  • 24
    • 0031541195 scopus 로고    scopus 로고
    • Continuation of blow-up solutions of nonlinear heat equations in several space dimensions
    • Galaktionov V A and Vazquez J L 1997 Continuation of blow-up solutions of nonlinear heat equations in several space dimensions Commun. Pure Appl. Math. 50 1-68
    • (1997) Commun. Pure Appl. Math. , vol.50 , pp. 1-68
    • Galaktionov, V.A.1    Vazquez, J.L.2
  • 25
    • 4744355066 scopus 로고    scopus 로고
    • A stability technique for evolution partial differential equations
    • Boston, MA: Birkhäuser
    • Galaktionov V A and Vazquez J L 2004 A Stability Technique for Evolution Partial Differential Equations. A Dynamical Systems Approach (Boston, MA: Birkhäuser)
    • (2004) A Dynamical Systems Approach
    • Galaktionov, V.A.1    Vazquez, J.L.2
  • 28
    • 46549093257 scopus 로고
    • Some infinite-dimensional Morse-Smale systems defined by parabolic partial differential equations
    • Henry D B 1985 Some infinite-dimensional Morse-Smale systems defined by parabolic partial differential equations J. Diff. Eqns 59 165-205
    • (1985) J. Diff. Eqns. , vol.59 , pp. 165-205
    • Henry, D.B.1
  • 29
    • 84968514121 scopus 로고
    • Singular solutions of the heat equation with absorption
    • Kamin S and Peletier L A 1985 Singular solutions of the heat equation with absorption Proc. Am. Math. Soc 95 205-10
    • (1985) Proc. Am. Math. Soc. , vol.95 , pp. 205-210
    • Kamin, S.1    Peletier, L.A.2
  • 30
    • 51249178019 scopus 로고
    • Large time behaviour of solutions of the porous media equation with absorption
    • Kamin S and Peletier L A 1986 Large time behaviour of solutions of the porous media equation with absorption Israel J. Math. 55 129-46
    • (1986) Israel J. Math. , vol.55 , pp. 129-146
    • Kamin, S.1    Peletier, L.A.2
  • 31
    • 51249172103 scopus 로고
    • Existence and uniqueness of the very singular solution of the porous media equation with absorption
    • Kamin S and Véron L 1988 Existence and uniqueness of the very singular solution of the porous media equation with absorption J. Anal. Math. 51 245-58
    • (1988) J. Anal. Math. , vol.51 , pp. 245-258
    • Kamin, S.1    Véron, L.2
  • 36
    • 0001192116 scopus 로고    scopus 로고
    • The Cahn-Hilliard equation: Mathematical and modeling perspectives
    • Novick-Cohen A 1998 The Cahn-Hilliard equation: mathematical and modeling perspectives Adv. Math. Sci. Appl. 8 965-85
    • (1998) Adv. Math. Sci. Appl. , vol.8 , pp. 965-985
    • Novick-Cohen, A.1
  • 37
    • 0001386608 scopus 로고
    • Nonlinear aspects of the Cahn-Hilliard equation
    • Novick-Cohen A and Segel L A 1984 Nonlinear aspects of the Cahn-Hilliard equation Physica D 10 277-98
    • (1984) Physica D , vol.10 , pp. 277-298
    • Novick-Cohen, A.1    Segel, L.A.2
  • 39
    • 0037373875 scopus 로고    scopus 로고
    • Global bifurcation for 2mth-order boundary value problems and infinitely many solutions of superlinear problems
    • Rynn B 2003 Global bifurcation for 2mth-order boundary value problems and infinitely many solutions of superlinear problems J. Diff. Eqns 188 461-72
    • (2003) J. Diff. Eqns. , vol.188 , pp. 461-472
    • Rynn, B.1
  • 41
    • 22844456779 scopus 로고    scopus 로고
    • Morse indices and exact multiplicity of solutions to semilinear elliptic problems
    • Shi J and Wang J 1999 Morse indices and exact multiplicity of solutions to semilinear elliptic problems Proc. Am. Math. Soc. 127 3685-95
    • (1999) Proc. Am. Math. Soc. , vol.127 , pp. 3685-3695
    • Shi, J.1    Wang, J.2
  • 43
    • 0001883857 scopus 로고
    • Stabilization of solutions of boundary value problems for a second order parabolic equation with one space variable
    • Zelenyak T I 1968 Stabilization of solutions of boundary value problems for a second order parabolic equation with one space variable J. Diff. Eqns 4 17-22
    • (1968) J. Diff. Eqns. , vol.4 , pp. 17-22
    • Zelenyak, T.I.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.