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Volumn 66, Issue 1, 2006, Pages 237-265

Existence and stability of traveling waves in buffered systems

Author keywords

Bistable equation; Calcium; FitzHugh Nagumo equations; Reaction diffusion equations; Stability; Traveling wave

Indexed keywords

CALCIUM; LINEAR EQUATIONS; PHYSIOLOGICAL MODELS; STABILITY; WAVE PROPAGATION; WAVEFRONTS;

EID: 33644603823     PISSN: 00361399     EISSN: None     Source Type: Journal    
DOI: 10.1137/040618291     Document Type: Article
Times cited : (35)

References (27)
  • 1
    • 0001203924 scopus 로고    scopus 로고
    • Existence, uniqueness, and asymptotic stability of traveling waves in nonlocal evolution equations
    • X. CHEN, Existence, uniqueness, and asymptotic stability of traveling waves in nonlocal evolution equations, Adv. Differential Equations, 2 (1997), pp. 125-160.
    • (1997) Adv. Differential Equations , vol.2 , pp. 125-160
    • Chen, X.1
  • 3
    • 0037215689 scopus 로고    scopus 로고
    • 2+ dynamics
    • 2+ dynamics, Biophys. J., 84 (2003), pp. 28-41.
    • (2003) Biophys. J. , vol.84 , pp. 28-41
    • Falcke, M.1
  • 4
    • 0003299218 scopus 로고
    • Mathematical aspects of reacting and diffusing systems
    • Springer-Verlag, New York
    • P. FIFE, Mathematical Aspects of Reacting and Diffusing Systems, Lecture Notes in Biomath. 28, Springer-Verlag, New York, 1979.
    • (1979) Lecture Notes in Biomath , vol.28
    • Fife, P.1
  • 5
    • 0017637590 scopus 로고
    • The approach of solutions of non-linear diffusion equations to traveling front solutions
    • P. C. FIFE AND J. B. MCLEOD, The approach of solutions of non-linear diffusion equations to traveling front solutions, Arch. Ration. Mech. Anal., 65 (1977), pp. 335-361.
    • (1977) Arch. Ration. Mech. Anal. , vol.65 , pp. 335-361
    • Fife, P.C.1    Mcleod, J.B.2
  • 7
    • 0039399074 scopus 로고
    • On traveling wave solutions of the Hodgkin-Huxley equations
    • S. P. HASTINGS, On traveling wave solutions of the Hodgkin-Huxley equations, Arch. Rational Mech. Anal., 60 (1976), pp. 229-257.
    • (1976) Arch. Rational Mech. Anal. , vol.60 , pp. 229-257
    • Hastings, S.P.1
  • 9
    • 0001543317 scopus 로고
    • Waves in excitable media
    • J. P. KEENER, Waves in excitable media, SIAM J. Appl. Math., 39 (1980), pp. 528-548.
    • (1980) SIAM J. Appl. Math. , vol.39 , pp. 528-548
    • Keener, J.P.1
  • 10
    • 0042337230 scopus 로고
    • The stability of traveling wave front solutions of a reaction-diffusion system
    • G. A. KLAASEN AND W. C. TROY, The stability of traveling wave front solutions of a reaction-diffusion system, SIAM J. Appl. Math., 41 (1981), pp. 145-167.
    • (1981) SIAM J. Appl. Math. , vol.41 , pp. 145-167
    • Klaasen, G.A.1    Troy, W.C.2
  • 13
    • 0030611092 scopus 로고    scopus 로고
    • 2+] at the mouth of a calcium channel
    • 2+] at the mouth of a calcium channel, J. Neurosci., 17 (1997), pp. 6961-73.
    • (1997) J. Neurosci. , vol.17 , pp. 6961-6973
    • Naraghi, M.1    Neher, E.2
  • 15
    • 0032435180 scopus 로고    scopus 로고
    • 2+ signals
    • 2+ signals, Cell Calcium, 24 (1998), pp. 345-57.
    • (1998) Cell Calcium , vol.24 , pp. 345-357
    • Neher, E.1
  • 16
    • 0027530592 scopus 로고
    • Time courses of calcium and calcium-bound buffers following calcium influx in a model cell
    • M. C. NOWYCKY AND M. J. PINTER, Time courses of calcium and calcium-bound buffers following calcium influx in a model cell, Biophys. J., 64 (1993), pp. 77-91.
    • (1993) Biophys. J. , vol.64 , pp. 77-91
    • Nowycky, M.C.1    Pinter, M.J.2
  • 17
    • 0002307123 scopus 로고
    • Qualitative theory of the FitzHugh-Nagumo equations
    • J. RAUCH AND J. SMOLLER, Qualitative theory of the FitzHugh-Nagumo equations, Advances in Math., 27 (1978), pp. 12-44.
    • (1978) Advances in Math. , vol.27 , pp. 12-44
    • Rauch, J.1    Smoller, J.2
  • 18
    • 0017630393 scopus 로고
    • Invariant sets for systems of partial differential equations I: Parabolic equations
    • R. REDHEFFER AND W. WALTER, Invariant sets for systems of partial differential equations I: Parabolic equations, Arch. Rational Mech. Anal., 67 (1978), pp. 41-52.
    • (1978) Arch. Rational Mech. Anal. , vol.67 , pp. 41-52
    • Redheffer, R.1    Walter, W.2
  • 20
    • 0025117718 scopus 로고
    • Calcium diffusion modeling in a spherical neuron: Relevance of buffering properties
    • F. SALA AND A. HERNÁNDEZ-CRUZ, Calcium diffusion modeling in a spherical neuron: Relevance of buffering properties, Biophys. J., 57 (1990), pp. 313-324.
    • (1990) Biophys. J. , vol.57 , pp. 313-324
    • Sala, F.1    Hernández-Cruz, A.2
  • 21
    • 0029732847 scopus 로고    scopus 로고
    • 2+ channel
    • 2+ channel, Biophys. J., 71 (1996), pp. 3064-3072.
    • (1996) Biophys. J. , vol.71 , pp. 3064-3072
    • Smith, G.D.1
  • 22
    • 0035183189 scopus 로고    scopus 로고
    • Asymptotic analysis of buffered calcium diffusion near a point source
    • G. D. SMITH, L. DAI, R. M. MIURA, AND A. SHERMAN, Asymptotic analysis of buffered calcium diffusion near a point source, SIAM J. Appl. Math., 61 (2001), pp. 1816-1838.
    • (2001) SIAM J. Appl. Math. , vol.61 , pp. 1816-1838
    • Smith, G.D.1    Dai, L.2    Miura, R.M.3    Sherman, A.4
  • 24
    • 0028845999 scopus 로고
    • Mechanisms of calcium oscillations and waves: A quantitative analysis
    • J. SNEYD, J. KEIZER, AND M. J. SANDERSON, Mechanisms of calcium oscillations and waves: A quantitative analysis, FASEB J., 9 (1995), pp. 1463-1472.
    • (1995) FASEB J. , vol.9 , pp. 1463-1472
    • Sneyd, J.1    Keizer, J.2    Sanderson, M.J.3
  • 25
    • 0032141593 scopus 로고    scopus 로고
    • Traveling waves in buffered systems: Applications to calcium waves
    • J. SNEYD, P. D. DALE, AND A. DUFFY, Traveling waves in buffered systems: Applications to calcium waves, SIAM J. Appl. Math., 58 (1998), pp. 1178-1192.
    • (1998) SIAM J. Appl. Math. , vol.58 , pp. 1178-1192
    • Sneyd, J.1    Dale, P.D.2    Duffy, A.3
  • 26
    • 45449123944 scopus 로고
    • Singular perturbation theory of traveling waves in excitable media
    • J. J. TYSON AND J. P. KEENER, Singular perturbation theory of traveling waves in excitable media, Phys. D, 32 (1988), pp. 327-361.
    • (1988) Phys. D , vol.32 , pp. 327-361
    • Tyson, J.J.1    Keener, J.P.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.