메뉴 건너뛰기




Volumn 259, Issue 2, 2008, Pages 287-309

Lyapunov functions and convergence to steady state for differential equations of fractional order

Author keywords

ojasiewicz inequality; Convergence to steady state; Fractional derivative; Gradient system; Integro differential equations; Lyapunov function

Indexed keywords


EID: 43349096659     PISSN: 00255874     EISSN: 14321823     Source Type: Journal    
DOI: 10.1007/s00209-007-0225-1     Document Type: Article
Times cited : (72)

References (25)
  • 1
    • 0346448287 scopus 로고    scopus 로고
    • Long-time stabilization of solutions to a phase-field model with memory
    • Aizicovici S. and Feireisl E. (2001). Long-time stabilization of solutions to a phase-field model with memory. J. Evol. Equ. 1: 69-84
    • (2001) J. Evol. Equ. , vol.1 , pp. 69-84
    • Aizicovici, S.1    Feireisl, E.2
  • 2
    • 33645139538 scopus 로고    scopus 로고
    • Asymptotic behavior of solutions of a conserved phase-field system with memory
    • Aizicovici S. and Petzeltová H. (2003). Asymptotic behavior of solutions of a conserved phase-field system with memory. J. Integral Equ. Appl. 15: 217-240
    • (2003) J. Integral Equ. Appl. , vol.15 , pp. 217-240
    • Aizicovici, S.1    Petzeltová, H.2
  • 3
    • 0038116267 scopus 로고    scopus 로고
    • On the Łojasiewicz-Simon gradient inequality
    • Chill R. (2003). On the Łojasiewicz-Simon gradient inequality. J. Funct. Anal. 201: 572-601
    • (2003) J. Funct. Anal. , vol.201 , pp. 572-601
    • Chill, R.1
  • 4
    • 12944249312 scopus 로고    scopus 로고
    • Convergence to steady states of solutions of semilinear evolutionary integral equations
    • Chill R. and Fašangová E. (2005). Convergence to steady states of solutions of semilinear evolutionary integral equations. Calc. Var. Partial Differ. Equ. 22: 321-342
    • (2005) Calc. Var. Partial Differ. Equ. , vol.22 , pp. 321-342
    • Chill, R.1    Fašangová, E.2
  • 5
    • 33749673101 scopus 로고    scopus 로고
    • Convergence to steady states of solutions of the Cahn-Hilliard equation with dynamic boundary conditions
    • to appear
    • Chill, R., Fašangová, E., Prüss, J.: Convergence to steady states of solutions of the Cahn-Hilliard equation with dynamic boundary conditions. Math. Nachr. (to appear) (2006)
    • (2006) Math. Nachr.
    • Chill, R.1    Fašangová, E.2    Prüss, J.3
  • 6
    • 43349101897 scopus 로고
    • On abstract Volterra equations in Banach spaces with completely positive kernels
    • Infinite-dimensional systems (Retzhof, 1983) Springer, Berlin
    • Clément, Ph.: On abstract Volterra equations in Banach spaces with completely positive kernels. Infinite-dimensional systems (Retzhof, 1983), pp. 32-40, Lecture Notes in Mathematics, vol. 1076. Springer, Berlin (1984)
    • (1984) Lecture Notes in Mathematics , vol.1076 , pp. 32-40
    • Clément, Ph.1
  • 7
    • 0041427064 scopus 로고
    • Asymptotic behavior of solutions of nonlinear Volterra equations with completely positive kernels
    • Clément Ph. and Nohel J.A. (1981). Asymptotic behavior of solutions of nonlinear Volterra equations with completely positive kernels. SIAM J. Math. Anal. 12: 514-535
    • (1981) SIAM J. Math. Anal. , vol.12 , pp. 514-535
    • Clément, Ph.1    Nohel, J.A.2
  • 8
    • 0002969970 scopus 로고
    • Completely positive measures and Feller semigroups
    • Clément Ph. and Prüss J. (1990). Completely positive measures and Feller semigroups. Math. Ann. 287: 73-105
    • (1990) Math. Ann. , vol.287 , pp. 73-105
    • Clément, Ph.1    Prüss, J.2
  • 9
    • 0001629395 scopus 로고
    • Asymptotic stability in viscoelasticity
    • Dafermos C.M. (1970). Asymptotic stability in viscoelasticity. Arch. Ration. Mech. Anal. 37: 297-308
    • (1970) Arch. Ration. Mech. Anal. , vol.37 , pp. 297-308
    • Dafermos, C.M.1
  • 10
    • 33645159827 scopus 로고    scopus 로고
    • Long time behavior of solutions to the Caginalp system with singular potential
    • Grasselli M., Petzeltová H. and Schimperna G. (2006). Long time behavior of solutions to the Caginalp system with singular potential. Z. Anal. Anwend. 25: 51-72
    • (2006) Z. Anal. Anwend. , vol.25 , pp. 51-72
    • Grasselli, M.1    Petzeltová, H.2    Schimperna, G.3
  • 11
    • 0011426570 scopus 로고
    • Volterra integro-differential equations with accretive nonlinearity
    • Gripenberg G. (1985). Volterra integro-differential equations with accretive nonlinearity. J. Differ. Equ. 60: 57-79
    • (1985) J. Differ. Equ. , vol.60 , pp. 57-79
    • Gripenberg, G.1
  • 13
    • 0002796050 scopus 로고    scopus 로고
    • Convergence of bounded weak solutions of the wave equation with dissipation and analytic nonlinearity
    • Haraux A. and Jendoubi M.A. (1999). Convergence of bounded weak solutions of the wave equation with dissipation and analytic nonlinearity. Calc. Var. Partial Differ. Equ. 9: 95-124
    • (1999) Calc. Var. Partial Differ. Equ. , vol.9 , pp. 95-124
    • Haraux, A.1    Jendoubi, M.A.2
  • 14
    • 0000746952 scopus 로고    scopus 로고
    • Convergence of solutions of second-order gradient-like systems with analytic nonlinearities
    • Haraux A. and Jendoubi M.A. (1998). Convergence of solutions of second-order gradient-like systems with analytic nonlinearities. J. Differ. Equ. 144: 313-320
    • (1998) J. Differ. Equ. , vol.144 , pp. 313-320
    • Haraux, A.1    Jendoubi, M.A.2
  • 16
    • 0000898687 scopus 로고    scopus 로고
    • Convergence of global and bounded solutions of the wave equation with linear dissipation and analytic nonlinearity
    • Jendoubi M.A. (1998). Convergence of global and bounded solutions of the wave equation with linear dissipation and analytic nonlinearity. J. Differ. Equ. 144: 302-312
    • (1998) J. Differ. Equ. , vol.144 , pp. 302-312
    • Jendoubi, M.A.1
  • 17
    • 0003366108 scopus 로고
    • Colloques internationaux du C.N.R.S.: Les Équations aux Dérivées Partielles, Paris, Éditions du C.N.R.S., Paris
    • Łojasiewicz, S.: Une propriété topologique des sous-ensembles analytiques réels. Colloques internationaux du C.N.R.S.: Les Équations aux Dérivées Partielles, Paris, Éditions du C.N.R.S., Paris, 1963, pp. 87-89 (1962)
    • (1962) Une Propriété Topologique des Sous-ensembles Analytiques Réels , pp. 87-89
    • Łojasiewicz, S.1
  • 20
    • 34250750395 scopus 로고    scopus 로고
    • p -regularity and long-time behaviour of the non-isothermal Cahn-Hilliard equation with dynamic boundary conditions
    • Partial differential equations and functional analysis Birkhäuser, Basel
    • p -regularity and long-time behaviour of the non-isothermal Cahn-Hilliard equation with dynamic boundary conditions. Partial differential equations and functional analysis, 209-236, Oper. Theory Adv. Appl., vol. 168. Birkhäuser, Basel (2006)
    • (2006) Oper. Theory Adv. Appl. , vol.168 , pp. 209-236
    • Prüss, J.1    Wilke, M.2
  • 22
    • 0000137102 scopus 로고
    • Asymptotics for a class of nonlinear evolution equations, with applications to geometric problems
    • 2
    • Simon L. (1983). Asymptotics for a class of nonlinear evolution equations, with applications to geometric problems. Ann. Math. 118(2): 525-571
    • (1983) Ann. Math. , vol.118 , pp. 525-571
    • Simon, L.1
  • 23
    • 42249083411 scopus 로고    scopus 로고
    • Thesis, Martin-Luther-Universität Halle, 2006. Published in Berichte aus der Mathematik, Shaker Verlag, Aachen
    • Vergara, V.: Convergence to steady state for a phase field system with memory. Thesis, Martin-Luther-Universität Halle, 2006. Published in Berichte aus der Mathematik, Shaker Verlag, Aachen (2006)
    • (2006) Convergence to Steady State for A Phase Field System with Memory
    • Vergara, V.1
  • 24
    • 17044365865 scopus 로고    scopus 로고
    • p for abstract parabolic Volterra equations
    • p for abstract parabolic Volterra equations. J. Evol. Equ. 5: 79-103
    • (2005) J. Evol. Equ. , vol.5 , pp. 79-103
    • Zacher, R.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.