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Volumn 9, Issue 5, 2010, Pages 1131-1160

Homogenization limit and asymptotic decay for electrical conduction in biological tissues in the high radiofrequency range

Author keywords

Dynamical boundary conditions; Electrical conduction in biological tissues; Homogenization; Oscillating test function method

Indexed keywords


EID: 84859540096     PISSN: 15340392     EISSN: 15535258     Source Type: Journal    
DOI: 10.3934/cpaa.2010.9.1131     Document Type: Conference Paper
Times cited : (18)

References (28)
  • 1
    • 84980080664 scopus 로고
    • Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary value conditions II
    • S. Agmon, A. Douglis and L. Nirenberg, Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary value conditions II, Comm. Pure and Appl. Math., 12 (1964), 35-92.
    • (1964) Comm. Pure and Appl. Math. , vol.12 , pp. 35-92
    • Agmon, S.1    Douglis, A.2    Nirenberg, L.3
  • 2
    • 0042170414 scopus 로고    scopus 로고
    • Homogenization limit for electrical conduction in biological tissues in the radio-frequency range
    • DOI 10.1016/S1631-0721(03)00107-4
    • M. Amar, D. Andreucci, P. Bisegna and R. Gianni, Homogenization limit for electrical conduction in biological tissues in the radio-frequency range, Comptes Rendus Mecanique, 331 (2003), 503-508. (Pubitemid 36934904)
    • (2003) Comptes Rendus - Mecanique , vol.331 , Issue.7 , pp. 503-508
    • Amar, M.1    Andreucci, D.2    Bisegna, P.3    Gianni, R.4
  • 3
    • 1842606510 scopus 로고    scopus 로고
    • An elliptic equation with history
    • DOI 10.1016/j.crma.2004.02.008, PII S1631073X04000901
    • M. Amar, D. Andreucci, P. Bisegna and R. Gianni, An elliptic equation with history, C. R. Acad. Sci. Paris, Ser. I, 338 (2004), 595-598. (Pubitemid 38457757)
    • (2004) Comptes Rendus Mathematique , vol.338 , Issue.8 , pp. 595-598
    • Amar, M.1    Andreucci, D.2    Bisegna, P.3    Gianni, R.4
  • 4
    • 1842512759 scopus 로고    scopus 로고
    • Evolution and memory effects in the homogenization limit for electrical conduction in biological tissues
    • DOI 10.1142/S0218202504003623
    • M. Amar, D. Andreucci, P. Bisegna and R. Gianni, Evolution and memory effects in the homogenization limit for electrical conduction in biological tissues, Math. Models Methods Appl. Sci., 14 (2004), 1261-1295. (Pubitemid 39436357)
    • (2004) Mathematical Models and Methods in Applied Sciences , vol.14 , Issue.9 , pp. 1261-1295
    • Amar, M.1    Andreucci, D.2    Gianni, R.3    Bisegna, P.4
  • 5
    • 33646187763 scopus 로고    scopus 로고
    • On a hierarchy of models for electrical conduction in biological tissues
    • M. Amar, D. Andreucci, P. Bisegna and R. Gianni, On a hierarchy of models for electrical conduction in biological tissues, Math. Methods Appl. Sci., 29 (2006), 767-787.
    • (2006) Math. Methods Appl. Sci. , vol.29 , pp. 767-787
    • Amar, M.1    Andreucci, D.2    Bisegna, P.3    Gianni, R.4
  • 6
    • 74049099715 scopus 로고    scopus 로고
    • Exponential asymptotic stability for an elliptic equation with memory arising in electrical conduction in biological tissues
    • M. Amar, D. Andreucci, P. Bisegna and R. Gianni, Exponential asymptotic stability for an elliptic equation with memory arising in electrical conduction in biological tissues, European J. Appl. Math., 20 (2009), 431-459.
    • (2009) European J. Appl. Math. , vol.20 , pp. 431-459
    • Amar, M.1    Andreucci, D.2    Bisegna, P.3    Gianni, R.4
  • 7
    • 70350375600 scopus 로고    scopus 로고
    • Stability and memory effects in a homogenized model governing the electrical conduction in biological tissues
    • M. Amar, D. Andreucci, P. Bisegna and R. Gianni, Stability and memory effects in a homogenized model governing the electrical conduction in biological tissues, J. Mechanics of Material and Structures, 4 (2009), 211-223.
    • (2009) J. Mechanics of Material and Structures , vol.4 , pp. 211-223
    • Amar, M.1    Andreucci, D.2    Bisegna, P.3    Gianni, R.4
  • 9
    • 33748171065 scopus 로고    scopus 로고
    • Bioimpedance tomography (electrical impedance tomography)
    • DOI 10.1146/annurev.bioeng.8.061505.095716
    • R. Bayford, Bioimpedance Tomography (Electrical Impedance Tomography), Annu. Rev. Biomed. Eng., 8 (2006), 63-91. (Pubitemid 44314813)
    • (2006) Annual Review of Biomedical Engineering , vol.8 , pp. 63-91
    • Bayford, R.H.1
  • 11
    • 0036904346 scopus 로고    scopus 로고
    • Electrical impedance tomography
    • L. Borcea, Electrical impedance tomography, Inverse Problems, 18 (2002), R99-R136.
    • (2002) Inverse Problems , vol.18
    • Borcea, L.1
  • 12
    • 0002621641 scopus 로고    scopus 로고
    • Electrical impedance tomography
    • PII S0036144598333613
    • M. Cheney, D. Isaacson and J. Newell, Electrical impedance tomography, SIAM Rev., 41 (1999), 85-101. (Pubitemid 129723749)
    • (1999) SIAM Review , vol.41 , Issue.1 , pp. 85-101
    • Cheney, M.1    Isaacson, D.2    Newell, J.C.3
  • 13
    • 33846887861 scopus 로고    scopus 로고
    • Homogenization of the wave equation in composites with imperfect interfaces: A memory effect
    • P. Donato, L. Faella and S. Monsurrò, Homogenization of the wave equation in composites with imperfect interfaces: A memory effect, J. Math. Pures Appl., 87 (2007), 119-143.
    • (2007) J. Math. Pures Appl. , vol.87 , pp. 119-143
    • Donato, P.1    Faella, L.2    Monsurrò, S.3
  • 14
    • 0023861304 scopus 로고
    • Viscoelastic relaxation functions compatible with thermodynamics
    • M. Fabrizio and A. Morro, Viscoelastic relaxation functions compatible with thermodynamics, J. Elasticity, 19 (1988), 63-75. (Pubitemid 18565457)
    • (1988) Journal of Elasticity , vol.19 , Issue.1 , pp. 63-75
    • Fabrizio, M.1    Morro, A.2
  • 15
    • 0007077515 scopus 로고
    • Avere una memoria tenace crea gravi problemi
    • G. Fichera, Avere una memoria tenace crea gravi problemi, Arch. Ration. Mech. Anal., 70 (1979), 101-112.
    • (1979) Arch. Ration. Mech. Anal. , vol.70 , pp. 101-112
    • Fichera, G.1
  • 16
    • 0008329457 scopus 로고    scopus 로고
    • Exponential stability in linear heat conduction with memory: A semigroup approach
    • C. Giorgi, M. Naso and V. Pata, Exponential stability in linear heat conduction with memory: a semigroup approach, Commun. Appl. Anal., 5 (2001), 121-133.
    • (2001) Commun. Appl. Anal. , vol.5 , pp. 121-133
    • Giorgi, C.1    Naso, M.2    Pata, V.3
  • 18
    • 33846881481 scopus 로고    scopus 로고
    • Homogenization for heat transfer in polycrystals with interfacial resistances
    • H.-K. Hummel, Homogenization for heat transfer in polycrystals with interfacial resistances, Appl. Anal., 75 (2000), 403-424.
    • (2000) Appl. Anal. , vol.75 , pp. 403-424
    • Hummel, H.-K.1
  • 19
    • 0026853864 scopus 로고
    • Sufficient conditions for the exponential stability in linear conductors with memory
    • B. Lazzari and R. Nibbi, Sufficient conditions for the exponential stability in linear conductors with memory, Int. J. Eng. Sci., 30 (1992), 533-544.
    • (1992) Int. J. Eng. Sci. , vol.30 , pp. 533-544
    • Lazzari, B.1    Nibbi, R.2
  • 20
    • 0036605015 scopus 로고    scopus 로고
    • Constitutive equations and quasi-static problem in linear thermoviscoelaticity
    • B. Lazzari and E. Vuk, Constitutive equations and quasi-static problem in linear thermoviscoelaticity, Int. J. Eng. Sci., 40 (2002), 1131-1149.
    • (2002) Int. J. Eng. Sci. , vol.40 , pp. 1131-1149
    • Lazzari, B.1    Vuk, E.2
  • 21
    • 0001498382 scopus 로고
    • Étude de l'influence d'un glissement entre les constituants d'un matériau composite sur ses coefficients de comportement effectifs
    • F. Lene and D. Leguillon, Étude de l'influence d'un glissement entre les constituants d'un matériau composite sur ses coefficients de comportement effectifs, Journal de Mécanique, 20 (1981), 509-536.
    • (1981) Journal de Mécanique , vol.20 , pp. 509-536
    • Lene, F.1    Leguillon, D.2
  • 22
    • 0032002569 scopus 로고    scopus 로고
    • Heat conduction in fine scale mixtures with interfacial contact resistance
    • PII S0036139995295153
    • R. Lipton, Heat conduction in fine scale mixtures with interfacial contact resistance, SIAM J. Appl. Math., 58 (1998), 55-72. (Pubitemid 128587702)
    • (1998) SIAM Journal on Applied Mathematics , vol.58 , Issue.1 , pp. 55-72
    • Lipton, R.1
  • 23
    • 25144463982 scopus 로고    scopus 로고
    • Asymptotic behavior for a viscoelastic problem with not necessarily decreasing kernel
    • DOI 10.1016/j.amc.2004.08.035, PII S0096300304005636
    • M. Medjden and N.-E. Tatar, Asymptotic behavior for a viscoelastic problem with not necessarily decreasing kernel, Appl. Math. Comput., 167 (2005), 1221-1235. (Pubitemid 41344820)
    • (2005) Applied Mathematics and Computation , vol.167 , Issue.2 , pp. 1221-1235
    • Medjden, M.1    Tatar, N.-E.2
  • 25
    • 34250112428 scopus 로고
    • Compact sets in the space lp(0, t; B)
    • J. Simon, Compact sets in the space lp(0, t; b), Ann. Mat. Pura Appl., 146 (1987), 65-96.
    • (1987) Ann. Mat. Pura Appl. , vol.146 , pp. 65-96
    • Simon, J.1
  • 26
    • 0019664632 scopus 로고
    • Global existence, uniqueness, and asymptotic stability of classical smooth solutions in one-dimensional nonlinear thermoelasticity
    • M. Slemrod, Global existence, uniqueness, and asymptotic stability of classical smooth solutions in one-dimensional nonlinear thermoelasticity, Arch. Ration. Mech. Anal., 76 (1981), 97-133. (Pubitemid 12513893)
    • (1981) Archive for Rational Mechanics and Analysis , vol.76 , Issue.2 , pp. 97-133
    • Slemrod, M.1
  • 28
    • 0004026738 scopus 로고
    • John Wiley & Sons, New York-Chichester-Brisbane, second edition
    • A. Taylor and D. Lay, " Introduction to Functional Analysis," John Wiley & Sons, New York-Chichester-Brisbane, second edition, 1980.
    • (1980) Introduction to Functional Analysis
    • Taylor, A.1    Lay, D.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.