메뉴 건너뛰기




Volumn 20, Issue 8, 2007, Pages 1773-1797

Finite-dimensionality of attractors for degenerate equations of elliptic-parabolic type

Author keywords

[No Author keywords available]

Indexed keywords


EID: 34547477219     PISSN: 09517715     EISSN: 13616544     Source Type: Journal    
DOI: 10.1088/0951-7715/20/8/001     Document Type: Article
Times cited : (15)

References (34)
  • 1
    • 0000836987 scopus 로고
    • Quasilinear elliptic-parabolic differential equations
    • Alt H W and Luckhaus S 1983 Quasilinear elliptic-parabolic differential equations Math. Z. 183 311-41
    • (1983) Math. Z. , vol.183 , Issue.3 , pp. 311-341
    • Alt, H.W.1    Luckhaus, S.2
  • 4
    • 0008563110 scopus 로고
    • Etude d'une équation doublement non linéaire
    • Bamberger A 1977 Etude d'une équation doublement non linéaire J. Funct. Anal. 24 148-55
    • (1977) J. Funct. Anal. , vol.24 , Issue.2 , pp. 148-155
    • Bamberger, A.1
  • 5
    • 0002092378 scopus 로고
    • A boundary modulus of continuity for a class of singular parabolic equations
    • DiBenedetto E 1986 A boundary modulus of continuity for a class of singular parabolic equations J. Diff. Eqns 63 418-47
    • (1986) J. Diff. Eqns , vol.63 , Issue.3 , pp. 418-447
    • Dibenedetto, E.1
  • 7
    • 0009386759 scopus 로고
    • Local behavior of solutions of an elliptic-parabolic equation
    • DiBenedetto E and Gariepy R 1987 Local behavior of solutions of an elliptic-parabolic equation Arch. Ration. Mech. Anal. 97 1-17
    • (1987) Arch. Ration. Mech. Anal. , vol.97 , pp. 1-17
    • Dibenedetto, E.1    Gariepy, R.2
  • 8
    • 0000132534 scopus 로고
    • Implicit degenerate evolution equations and applications
    • DiBenedetto E and Showalter R E 1981 Implicit degenerate evolution equations and applications SIAM. J. Math. Anal. 12 731-51
    • (1981) SIAM. J. Math. Anal. , vol.12 , Issue.5 , pp. 731-751
    • Dibenedetto, E.1    Showalter, R.E.2
  • 9
    • 67649306574 scopus 로고    scopus 로고
    • Current issues on singular and degenerate evolution equations
    • DiBenedetto E, Urbano J M and Vespri V 2004 Current issues on singular and degenerate evolution equations Evolutionary Equations (Handbook on Differential Equations) vol 1 (Amsterdam: North-Holland) pp 169-286
    • (2004) Evolutionary Equations , vol.1 , pp. 169-286
    • Dibenedetto, E.1    Urbano, J.M.2    Vespri, V.3
  • 12
    • 0003087307 scopus 로고
    • Doubly nonlinear parabolic-type equations as dynamical systems
    • Eden A, Michaux B and Rakotoson J-M 1991 Doubly nonlinear parabolic-type equations as dynamical systems J. Dyn. Diff. Eqns 3 87-131
    • (1991) J. Dyn. Diff. Eqns , vol.3 , Issue.1 , pp. 87-131
    • Eden, A.1    Michaux, B.2    Rakotoson, J.-M.3
  • 13
    • 0242421408 scopus 로고
    • Exponential attractors for a doubly nonlinear equation
    • Eden A and Rakotoson J-M 1994 Exponential attractors for a doubly nonlinear equation J. Math. Anal. Appl. 185 321-39
    • (1994) J. Math. Anal. Appl. , vol.185 , Issue.2 , pp. 321-339
    • Eden, A.1    Rakotoson, J.-M.2
  • 14
    • 0034654792 scopus 로고    scopus 로고
    • Exponential attractors for a nonlinear reaction-diffusion system in
    • Efendiev M, Miranville A and Zelik S 2000 Exponential attractors for a nonlinear reaction-diffusion system in C. R. Acad. Sci. Paris 330 713-18
    • (2000) C. R. Acad. Sci. Paris , vol.330 , pp. 713-718
    • Efendiev, M.1    Miranville, A.2    Zelik, S.3
  • 15
    • 34547470940 scopus 로고    scopus 로고
    • Finite and infinite dimensional attractors for porous media equations
    • Efendiev M and Zelik S Finite and infinite dimensional attractors for porous media equations Proc. R. Soc. Lond. A submitted
    • Proc. R. Soc. Lond.
    • Efendiev, M.1    Zelik, S.2
  • 17
    • 0002973412 scopus 로고
    • Sur la résolution d'une équation et d'une inéquation paraboliques non linéaires
    • Grange O and Mignot F 1972 Sur la résolution d'une équation et d'une inéquation paraboliques non linéaires J. Funct. Anal. 11 77-92
    • (1972) J. Funct. Anal. , vol.11 , Issue.1 , pp. 77-92
    • Grange, O.1    Mignot, F.2
  • 18
    • 0001158204 scopus 로고    scopus 로고
    • Generalized Ginzburg-Landau and Cahn-Hilliard equations based on a microforce balance
    • Gurtin M 1996 Generalized Ginzburg-Landau and Cahn-Hilliard equations based on a microforce balance Physica D 92 178-92
    • (1996) Physica , vol.92 , Issue.3-4 , pp. 178-192
    • Gurtin, M.1
  • 19
    • 51249191546 scopus 로고
    • Schrödinger operators with singular potentials
    • Kato T 1973 Schrödinger operators with singular potentials Israel J. Math. 13 135-48
    • (1973) Israel J. Math. , vol.13 , pp. 135-148
    • Kato, T.1
  • 20
    • 34250139358 scopus 로고
    • Kato's inequality for secondary-quantization operators
    • Kondrat'ev Yu G 1983 Kato's inequality for secondary-quantization operators Ukrainian Math. J. 35 656-9
    • (1983) Ukrainian Math. J. , vol.35 , Issue.6 , pp. 656-659
    • Kondrat'Ev Yu, G.1
  • 23
    • 0037141639 scopus 로고    scopus 로고
    • Large time behavior via the method of l-trajectories
    • Málek J and Praák D 2002 Large time behavior via the method of l-trajectories J. Diff. Eqns 181 243-79
    • (2002) J. Diff. Eqns , vol.181 , Issue.2 , pp. 243-279
    • Málek, J.1    Praák, D.2
  • 24
    • 1642337137 scopus 로고    scopus 로고
    • Robust exponential attractors for Cahn-Hilliard type equations with singular potentials
    • Miranville A and Zelik S 2004 Robust exponential attractors for Cahn-Hilliard type equations with singular potentials Math. Methods Appl. Sci. 27 545-82
    • (2004) Math. Methods Appl. Sci. , vol.27 , Issue.5 , pp. 545-582
    • Miranville, A.1    Zelik, S.2
  • 25
    • 33748847128 scopus 로고    scopus 로고
    • Finite dimensional global attractor for a class of doubly nonlinear parabolic equations
    • Miranville A 2006 Finite dimensional global attractor for a class of doubly nonlinear parabolic equations Cent. Eur. J. Math. 4 163-82
    • (2006) Cent. Eur. J. Math. , vol.4 , Issue.1 , pp. 163-182
    • Miranville, A.1
  • 26
    • 0030579044 scopus 로고    scopus 로고
    • 1-contraction and uniqueness for quasilinear elliptic-parabolic equations
    • 1-contraction and uniqueness for quasilinear elliptic-parabolic equations J. Diff. Eqns. 131 20-38
    • (1996) J. Diff. Eqns. , vol.131 , Issue.1 , pp. 20-38
    • Otto, F.1
  • 27
    • 0000854377 scopus 로고
    • Sur la résolution de certaines équations paraboliques non linéaires
    • Raviart P-A 1970 Sur la résolution de certaines équations paraboliques non linéaires J. Funct. Anal. 5 299-328
    • (1970) J. Funct. Anal. , vol.5 , Issue.2 , pp. 299-328
    • Raviart, P.-A.1
  • 29
    • 33645774239 scopus 로고    scopus 로고
    • Large time behavior for doubly nonlinear systems generated by subdifferentials
    • Shirakawa K 2000 Large time behavior for doubly nonlinear systems generated by subdifferentials Adv. Math. Sci. Appl. 10 77-92
    • (2000) Adv. Math. Sci. Appl. , vol.10 , pp. 77-92
    • Shirakawa, K.1
  • 30
    • 0001518364 scopus 로고
    • An abstract Kato's inequality for generators of positivity preserving semigroups
    • Simon B 1977 An abstract Kato's inequality for generators of positivity preserving semigroups Indiana Univ. Math. J. 26 1067-73
    • (1977) Indiana Univ. Math. J. , vol.26 , Issue.6 , pp. 1067-1073
    • Simon, B.1
  • 31
    • 21844495223 scopus 로고
    • Linking anisotropic sharp and diffuse surface motion laws via gradient flows
    • Taylor J E and Cahn J W 1994 Linking anisotropic sharp and diffuse surface motion laws via gradient flows J. Stat. Phys. 77 183-97
    • (1994) J. Stat. Phys. , vol.77 , Issue.1-2 , pp. 183-197
    • Taylor, J.E.1    Cahn, J.W.2
  • 33
    • 4944233120 scopus 로고    scopus 로고
    • Asymptotic regularity of solutions of singularly perturbed damped wave equations with supercritical nonlinearities
    • Zelik S 2004 Asymptotic regularity of solutions of singularly perturbed damped wave equations with supercritical nonlinearities Discrete Contin. Dyn. Syst. 11 351-92
    • (2004) Discrete Contin. Dyn. Syst. , vol.11 , pp. 351-392
    • Zelik, S.1
  • 34
    • 0037256259 scopus 로고    scopus 로고
    • Attractors of reaction-diffusion systems in unbounded domains and their spatial complexity
    • Zelik S 2003 Attractors of reaction-diffusion systems in unbounded domains and their spatial complexity Commun. Pure. Appl. Math. 56 584-637
    • (2003) Commun. Pure. Appl. Math. , vol.56 , Issue.5 , pp. 584-637
    • Zelik, S.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.