메뉴 건너뛰기




Volumn 317, Issue 2, 2006, Pages 381-397

Symmetries and solutions to the thin film equations

Author keywords

Generalized conditional symmetry; Rotation group; Scaling group; Thin film equation

Indexed keywords


EID: 33644589322     PISSN: 0022247X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jmaa.2005.07.040     Document Type: Article
Times cited : (28)

References (38)
  • 1
    • 0040573839 scopus 로고
    • Singularities in a modified Kuramoto-Sivashinsky equation describing interface motion for phase transition
    • A.J. Bernoff A.L. Bertozzi Singularities in a modified Kuramoto-Sivashinsky equation describing interface motion for phase transition Phys. D 85 1995 375-404
    • (1995) Phys. D , vol.85 , pp. 375-404
    • Bernoff, A.J.1    Bertozzi, A.L.2
  • 2
    • 0000999835 scopus 로고
    • An intrinsic equation of interfacial motion for the solidification of a pure hypercooled melt
    • D.C. Sarocka A.J. Bernoff An intrinsic equation of interfacial motion for the solidification of a pure hypercooled melt Phys. D 85 1995 348-374
    • (1995) Phys. D , vol.85 , pp. 348-374
    • Sarocka, D.C.1    Bernoff, A.J.2
  • 3
    • 0000507179 scopus 로고
    • Persistent propagation of concentration waves in dissipative media far from thermal equilibrium
    • Y. Kuramoto T. Tsuzuki Persistent propagation of concentration waves in dissipative media far from thermal equilibrium Progr. Theoret. Phys. 55 1976 356-369
    • (1976) Progr. Theoret. Phys. , vol.55 , pp. 356-369
    • Kuramoto, Y.1    Tsuzuki, T.2
  • 4
    • 0017554878 scopus 로고    scopus 로고
    • Nonlinear analysis of hydrodynamic instability in laminar flames I. Derivation of basic equations
    • G.I. Sivashinsky Nonlinear analysis of hydrodynamic instability in laminar flames I. Derivation of basic equations Acta Astronautica 4 1997 1177-1206
    • (1997) Acta Astronautica , vol.4 , pp. 1177-1206
    • Sivashinsky, G.I.1
  • 5
    • 0040865778 scopus 로고    scopus 로고
    • Pattern formation in a suspension of swimming micro-organisms: Nonlinear aspects
    • unpublished manuscript
    • S. Childress, E. Spiegel, Pattern formation in a suspension of swimming micro-organisms: Nonlinear aspects, unpublished manuscript
    • Childress, S.1    Spiegel, E.2
  • 6
    • 0039679737 scopus 로고
    • The large-scale structure of compressible convection
    • M.C. Depassier E. Spiegel The large-scale structure of compressible convection Astronom. J. 86 1981 496-512
    • (1981) Astronom. J. , vol.86 , pp. 496-512
    • Depassier, M.C.1    Spiegel, E.2
  • 7
    • 0020778244 scopus 로고
    • On cellular instability in the solidification of a dilate binary alloy
    • G.I. Sivashinsky On cellular instability in the solidification of a dilate binary alloy Phys. D 8 1983 243-248
    • (1983) Phys. D , vol.8 , pp. 243-248
    • Sivashinsky, G.I.1
  • 8
    • 0032368532 scopus 로고    scopus 로고
    • Long-wave instabilities and saturation in thin film equations
    • A.L. Bertozzi M.C. Pugh Long-wave instabilities and saturation in thin film equations Comm. Pure Appl. Math. 51 1998 625-661
    • (1998) Comm. Pure Appl. Math. , vol.51 , pp. 625-661
    • Bertozzi, A.L.1    Pugh, M.C.2
  • 9
    • 26544454798 scopus 로고
    • On KS-type equations describing the evolution and rupture of a liquid interface
    • T. Hocherman P. Rosenau On KS-type equations describing the evolution and rupture of a liquid interface Phys. D 67 1993 113-1254
    • (1993) Phys. D , vol.67 , pp. 113-1254
    • Hocherman, T.1    Rosenau, P.2
  • 10
    • 33644592124 scopus 로고    scopus 로고
    • On a modified Kuramoto-Sivashinsky equation
    • K.S. Chou On a modified Kuramoto-Sivashinsky equation Differential Integral Equations 15 2002 863-874
    • (2002) Differential Integral Equations , vol.15 , pp. 863-874
    • Chou, K.S.1
  • 11
    • 0001141126 scopus 로고
    • On Cahn-Hilliard type equations
    • A. Novick-Cohen On Cahn-Hilliard type equations Nonlinear Anal. 15 1990 797-814
    • (1990) Nonlinear Anal. , vol.15 , pp. 797-814
    • Novick-Cohen, A.1
  • 12
    • 0001343091 scopus 로고    scopus 로고
    • The viscous Cahn-Hilliard equation: Morse decompositions and structure of the global attractor
    • M. Grinfeld A. Novick-Cohen The viscous Cahn-Hilliard equation: Morse decompositions and structure of the global attractor Trans. Amer. Math. Soc. 351 1999 2375-2406
    • (1999) Trans. Amer. Math. Soc. , vol.351 , pp. 2375-2406
    • Grinfeld, M.1    Novick-Cohen, A.2
  • 16
    • 0000478462 scopus 로고
    • The general similarity solution of the heat equation
    • G.W. Bluman J.D. Cole The general similarity solution of the heat equation J. Math. Mech. 18 1969 1025-1042
    • (1969) J. Math. Mech. , vol.18 , pp. 1025-1042
    • Bluman, G.W.1    Cole, J.D.2
  • 17
    • 18944400520 scopus 로고
    • New similarity reductions of the Boussinesq equations
    • P.A. Clarkson M.D. Kruskal New similarity reductions of the Boussinesq equations J. Math. Phys. 30 1989 2201-2213
    • (1989) J. Math. Phys. , vol.30 , pp. 2201-2213
    • Clarkson, P.A.1    Kruskal, M.D.2
  • 18
    • 24844461457 scopus 로고
    • A note on the new similarity reductions of the Boussinesq equation
    • S.Y. Lou A note on the new similarity reductions of the Boussinesq equation Phys. Lett. A 151 1990 133-135
    • (1990) Phys. Lett. A , vol.151 , pp. 133-135
    • Lou, S.Y.1
  • 19
    • 0000393202 scopus 로고
    • The direct method and the singular manifold method for the Fitzhugh-Nagumo equation
    • P.G. Estevez The direct method and the singular manifold method for the Fitzhugh-Nagumo equation Phys. Lett. A 171 1992 259-261
    • (1992) Phys. Lett. A , vol.171 , pp. 259-261
    • Estevez, P.G.1
  • 20
    • 0002570098 scopus 로고
    • Anti-reduction and exact solutions of nonlinear heat equations
    • W.I. Fuschych R.Z. Zhdanov Anti-reduction and exact solutions of nonlinear heat equations J. Nonlinear Math. Phys. 1 1994 60-64
    • (1994) J. Nonlinear Math. Phys. , vol.1 , pp. 60-64
    • Fuschych, W.I.1    Zhdanov, R.Z.2
  • 21
    • 12044249804 scopus 로고
    • Nonlinear interaction of traveling waves of nonintegrable equations
    • A.S. Fokas Q.M. Liu Nonlinear interaction of traveling waves of nonintegrable equations Phys. Rev. Lett. 72 1994 3293-3296
    • (1994) Phys. Rev. Lett. , vol.72 , pp. 3293-3296
    • Fokas, A.S.1    Liu, Q.M.2
  • 22
    • 21844486280 scopus 로고
    • Conditional Lie-Bäcklund symmetry and reduction of evolution equation
    • R.Z. Zhdanov Conditional Lie-Bäcklund symmetry and reduction of evolution equation J. Phys. A 28 1995 3841-3850
    • (1995) J. Phys. A , vol.28 , pp. 3841-3850
    • Zhdanov, R.Z.1
  • 23
    • 0001290663 scopus 로고    scopus 로고
    • Group classification and generalized conditional symmetry reduction of the nonlinear diffusion-convection equation with a nonlinear source
    • C.Z. Qu Group classification and generalized conditional symmetry reduction of the nonlinear diffusion-convection equation with a nonlinear source Stud. Appl. Math. 99 1997 107-136
    • (1997) Stud. Appl. Math. , vol.99 , pp. 107-136
    • Qu, C.Z.1
  • 24
    • 6544263763 scopus 로고    scopus 로고
    • Exact solution to nonlinear diffusion equations obtained by a generalized conditional symmetry method
    • C.Z. Qu Exact solution to nonlinear diffusion equations obtained by a generalized conditional symmetry method IMA J. Appl. Math. 62 1999 283-302
    • (1999) IMA J. Appl. Math. , vol.62 , pp. 283-302
    • Qu, C.Z.1
  • 25
    • 0039592610 scopus 로고    scopus 로고
    • Separation of variables and exact solutions to quasilinear diffusion equations with nonlinear source
    • C.Z. Qu S.L. Zhang R.C. Liu Separation of variables and exact solutions to quasilinear diffusion equations with nonlinear source Phys. D 144 2000 97-123
    • (2000) Phys. D , vol.144 , pp. 97-123
    • Qu, C.Z.1    Zhang, S.L.2    Liu, R.C.3
  • 26
    • 0035796132 scopus 로고    scopus 로고
    • Analysis of a lubrication model through symmetry reductions
    • M.L. Gandarias E. Medina Analysis of a lubrication model through symmetry reductions Europhys. Lett. 55 2000 143-149
    • (2000) Europhys. Lett. , vol.55 , pp. 143-149
    • Gandarias, M.L.1    Medina, E.2
  • 27
    • 0346614819 scopus 로고    scopus 로고
    • Nonclassical symmetries for a family of Cahn-Hilliard equations
    • M.L. Gandarias M.S. Bruzon Nonclassical symmetries for a family of Cahn-Hilliard equations Phys. Lett. A 263 1999 331-337
    • (1999) Phys. Lett. A , vol.263 , pp. 331-337
    • Gandarias, M.L.1    Bruzon, M.S.2
  • 28
    • 0034239340 scopus 로고    scopus 로고
    • Symmetry analysis and solutions for a family of Cahn-Hilliard equations
    • M. L Gandarias M.S. Bruzon Symmetry analysis and solutions for a family of Cahn-Hilliard equations Rep. Math. Phys. 46 2000 89-97
    • (2000) Rep. Math. Phys. , vol.46 , pp. 89-97
    • Gandarias, M.L.1    Bruzon, M.S.2
  • 29
    • 0011911602 scopus 로고    scopus 로고
    • Groups of scalings and invariant sets for higher-order nonlinear evolution equations
    • V.A. Galaktionov Groups of scalings and invariant sets for higher-order nonlinear evolution equations Differential Integral Equations 14 2001 913-924
    • (2001) Differential Integral Equations , vol.14 , pp. 913-924
    • Galaktionov, V.A.1
  • 30
    • 0011831265 scopus 로고    scopus 로고
    • Ordered invariant sets for nonlinear evolution equations of KdV-type
    • V.A. Galaktionov Ordered invariant sets for nonlinear evolution equations of KdV-type Comput. Math. Math. Phys. 39 1999 1564-1570
    • (1999) Comput. Math. Math. Phys. , vol.39 , pp. 1564-1570
    • Galaktionov, V.A.1
  • 31
    • 0037408902 scopus 로고    scopus 로고
    • Extended rotation and scaling groups for nonlinear evolution equations
    • C.Z. Qu P.G. Estevez Extended rotation and scaling groups for nonlinear evolution equations Nonlinear Anal. 52 2003 1655-1673
    • (2003) Nonlinear Anal. , vol.52 , pp. 1655-1673
    • Qu, C.Z.1    Estevez, P.G.2
  • 32
    • 0005439285 scopus 로고    scopus 로고
    • Reductions and exact solutions of some nonlinear partial differential equations under four types of generalized conditional symmetries
    • C.Z. Qu Reductions and exact solutions of some nonlinear partial differential equations under four types of generalized conditional symmetries J. Aust. Math. Soc. B 41 1999 1-40
    • (1999) J. Aust. Math. Soc. B , vol.41 , pp. 1-40
    • Qu, C.Z.1
  • 33
    • 0034301969 scopus 로고    scopus 로고
    • Classification and reduction of some systems of quasilinear partial differential equations
    • C.Z. Qu Classification and reduction of some systems of quasilinear partial differential equations Nonlinear Anal. 42 2000 301-327
    • (2000) Nonlinear Anal. , vol.42 , pp. 301-327
    • Qu, C.Z.1
  • 34
    • 0347622670 scopus 로고    scopus 로고
    • New variable separation approach: Application to nonlinear diffusion equations
    • S.L. Zhang S.Y. Lou C.Z. Qu New variable separation approach: application to nonlinear diffusion equations J. Phys. A 36 2003 12223-12242
    • (2003) J. Phys. A , vol.36 , pp. 12223-12242
    • Zhang, S.L.1    Lou, S.Y.2    Qu, C.Z.3
  • 35
    • 2442570967 scopus 로고    scopus 로고
    • On nonlinear diffusion equations with x-dependent convection and absorption
    • C.Z. Qu P.G. Estevez On nonlinear diffusion equations with x-dependent convection and absorption Nonlinear Anal. 57 2004 549-577
    • (2004) Nonlinear Anal. , vol.57 , pp. 549-577
    • Qu, C.Z.1    Estevez, P.G.2
  • 36
    • 0034384058 scopus 로고    scopus 로고
    • The method of generalized conditional symmetries and its various implementations
    • J.M. Goard The method of generalized conditional symmetries and its various implementations European J. Appl. Math. 11 2000 215-224
    • (2000) European J. Appl. Math. , vol.11 , pp. 215-224
    • Goard, J.M.1
  • 37
    • 0035582578 scopus 로고    scopus 로고
    • Initial-value problems for evolution partial differential equations and higher-order conditional symmetries
    • P. Basarab-Horwath R.Z. Zhdanov Initial-value problems for evolution partial differential equations and higher-order conditional symmetries J. Math. Phys. 42 2001 376-389
    • (2001) J. Math. Phys. , vol.42 , pp. 376-389
    • Basarab-Horwath, P.1    Zhdanov, R.Z.2
  • 38
    • 0036537869 scopus 로고    scopus 로고
    • Higher conditional symmetry and reduction of initial value problems
    • R.Z. Zhdanov Higher conditional symmetry and reduction of initial value problems Nonlinear Dynam. 28 2002 17-27
    • (2002) Nonlinear Dynam. , vol.28 , pp. 17-27
    • Zhdanov, R.Z.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.