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Volumn 11, Issue 3, 2005, Pages 487-507

Asymptotic stability of linear conservative systems when coupled with diffusive systems

Author keywords

Asymptotic stability; Diffusive representation; Fractional calculus; Lyapunov functional; Well posed systems

Indexed keywords

ASYMPTOTIC STABILITY; COMPUTATION THEORY; DIMENSIONAL STABILITY; LYAPUNOV METHODS; OPTIMIZATION; VARIATIONAL TECHNIQUES;

EID: 30844468636     PISSN: 12928119     EISSN: 12623377     Source Type: Journal    
DOI: 10.1051/cocv:2005016     Document Type: Article
Times cited : (29)

References (25)
  • 1
    • 84966249611 scopus 로고
    • Tauberian theorems and stability of one-parameter semigroups
    • W. Arendt and C.J.K. Batty, Tauberian theorems and stability of one-parameter semigroups. Trans. Am. Math. Soc. 306 (1988) 837-852.
    • (1988) Trans. Am. Math. Soc , vol.306 , pp. 837-852
    • Arendt, W.1    Batty, C.J.K.2
  • 3
    • 0009618266 scopus 로고
    • General formulation of the dispersion equation in bounded viscothermal fluid, and application to some simple geometries
    • M. Bruneau, Ph. Herzog, J. Kergomard and J.-D. Polack, General formulation of the dispersion equation in bounded viscothermal fluid, and application to some simple geometries. Wave Motion 11 (1989) 441-451.
    • (1989) Wave Motion , vol.11 , pp. 441-451
    • Bruneau, M.1    Herzog, P.H.2    Kergomard, J.3    Polack, J.-D.4
  • 5
    • 85011665196 scopus 로고
    • Stabilization of second order evolution equations by unbounded nonlinear feedback
    • F. Conrad and M. Pierre, Stabilization of second order evolution equations by unbounded nonlinear feedback. Ann. Inst. Henri Poincaré, Anal. Non Linéaire 11 (1994) 485-515.
    • (1994) Ann. Inst. Henri Poincaré, Anal. Non Linéaire , vol.11 , pp. 485-515
    • Conrad, F.1    Pierre, M.2
  • 6
    • 0001773481 scopus 로고
    • An introduction to infinite-dimensional linear systems theory
    • R.F. Curtain and H. Zwart, An introduction to infinite-dimensional linear systems theory. Texts Appl. Math. 21 (1995).
    • (1995) Texts Appl. Math. , pp. 21
    • Curtain, R.F.1    Zwart, H.2
  • 9
    • 1642366889 scopus 로고    scopus 로고
    • Direct and inverse scattering problem in porous material having a rigid frame by fractional calculus based method
    • Z.E.A. Fellah, C. Depollier and M. Fellah, Direct and inverse scattering problem in porous material having a rigid frame by fractional calculus based method. J. Sound Vibration 244 (2001) 3659-3666.
    • (2001) J. Sound Vibration , vol.244 , pp. 3659-3666
    • Fellah, Z.E.A.1    Depollier, C.2    Fellah, M.3
  • 11
    • 0242440805 scopus 로고    scopus 로고
    • Unidimensional models of acoustic propagation in axisymmetric waveguides
    • Th. Helie, Unidimensional models of acoustic propagation in axisymmetric waveguides. J. Acoust. Soc. Am. 114 (2003) 2633-2647.
    • (2003) J. Acoust. Soc. Am , vol.114 , pp. 2633-2647
    • Helie, T.H.1
  • 12
    • 84960608350 scopus 로고
    • On Wiener’s method in Tauberian theorems, in
    • A.E. Ingham, On Wiener’s method in Tauberian theorems, in Proc. London Math. Soc. II 38 (1935) 458-480.
    • (1935) Proc. London Math. Soc. II , vol.38 , pp. 458-480
    • Ingham, A.E.1
  • 13
    • 0001325228 scopus 로고
    • On Newman’s quick way to the prime number theorem
    • J. Korevaar, On Newman’s quick way to the prime number theorem. Math. Intell. 4 (1982) 108-115.
    • (1982) Math. Intell. , vol.4 , pp. 108-115
    • Korevaar, J.1
  • 14
    • 0012474708 scopus 로고
    • Wave equation with singular retarded time
    • (in Russian)
    • A.A. Lokshin, Wave equation with singular retarded time. Dokl. Akad. Nauk SSSR 240 (1978) 43-46 (in Russian).
    • (1978) Dokl. Akad. Nauk SSSR , vol.240 , pp. 43-46
    • Lokshin, A.A.1
  • 15
    • 0000911022 scopus 로고
    • Fundamental solutions of the wave equation with retarded time
    • (in Russian)
    • A.A. Lokshin and V.E. Rok, Fundamental solutions of the wave equation with retarded time. Dokl. Akad. Nauk SSSR 239(1978) 1305-1308 (in Russian).
    • (1978) Dokl. Akad. Nauk SSSR , vol.239 , pp. 1305-1308
    • Lokshin, A.A.1    Rok, V.E.2
  • 16
    • 0003556556 scopus 로고    scopus 로고
    • Stability and stabilization of infinite dimensional systems and applications
    • Springer-Verlag, New York
    • Z.-H. Luo, B.-Z. Guo and O. Morgul, Stability and stabilization of infinite dimensional systems and applications. Comm. Control Engrg. Springer-Verlag, New York (1999).
    • (1999) Comm. Control Engrg
    • Luo, Z.-H.1    Guo, B.-Z.2    Morgul, O.3
  • 17
    • 0003090139 scopus 로고
    • Asymptotic stability of linear differential equations in Banach spaces
    • Yu.I. Lyubich and V.Q. Phong, Asymptotic stability of linear differential equations in Banach spaces. Stud. Math. 88 (1988)37-42.
    • (1988) Stud. Math. , vol.88 , pp. 37-42
    • Lyubich, Y.1    Phong, V.Q.2
  • 18
    • 0000074512 scopus 로고    scopus 로고
    • Stability properties for generalized fractional differential systems
    • D. Matignon, Stability properties for generalized fractional differential systems. ESAIM: Proc. 5 (1998) 145-158.
    • (1998) ESAIM: Proc , vol.5 , pp. 145-158
    • Matignon, D.1
  • 19
    • 0001752652 scopus 로고    scopus 로고
    • Diffusive representation of pseudo-differential time-operators
    • G. Montseny, Diffusive representation of pseudo-differential time-operators. ESAIM: Proc. 5 (1998) 159-175.
    • (1998) ESAIM: Proc , vol.5 , pp. 159-175
    • Montseny, G.1
  • 20
    • 0010783750 scopus 로고
    • Simple analytic proof of the prime number theorem
    • D.J. Newman, Simple analytic proof of the prime number theorem. Am. Math. Mon. 87 (1980) 693-696.
    • (1980) Am. Math. Mon. , vol.87 , pp. 693-696
    • Newman, D.J.1
  • 21
    • 0000702465 scopus 로고
    • Time domain solution of Kirchhoff’s equation for sound propagation in viscothermal gases: A diffusion process
    • J.-D. Polack, Time domain solution of Kirchhoff’s equation for sound propagation in viscothermal gases: a diffusion process. J. Acoustique 4 (1991) 47-67.
    • (1991) J. Acoustique , vol.4 , pp. 47-67
    • Polack, J.-D.1
  • 22
    • 0008690325 scopus 로고
    • Well-posedness and stabilizability of a viscoelastic equation in energy space
    • O.J. Staffans, Well-posedness and stabilizability of a viscoelastic equation in energy space. Trans. Am. Math. Soc. 345 (1994)527-575.
    • (1994) Trans. Am. Math. Soc. , vol.345 , pp. 527-575
    • Staffans, O.J.1
  • 23
    • 0036944083 scopus 로고    scopus 로고
    • Passive and conservative continuous-time impedance and scattering systems. Part I: Well-posed systems
    • O.J. Staffans, Passive and conservative continuous-time impedance and scattering systems. Part I: Well-posed systems. Math. Control Sig. Syst. 15 (2002) 291-315.
    • (2002) Math. Control Sig. Syst. , vol.15 , pp. 291-315
    • Staffans, O.J.1
  • 24
  • 25
    • 2942536559 scopus 로고    scopus 로고
    • How to get a conservative well-posed linear system out of thin air. Part I. Well-posedness and energy balance
    • G. Weiss and M. Tucsnak, How to get a conservative well-posed linear system out of thin air. Part I. Well-posedness and energy balance. ESAIM: COCV 9 (2003) 247-273.
    • (2003) ESAIM: COCV , vol.9 , pp. 247-273
    • Weiss, G.1    Tucsnak, M.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.