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Volumn 464, Issue 2098, 2008, Pages 2591-2608

Uniqueness of fast travelling fronts in reaction-diffusion equations with delay

Author keywords

Monostable case; Single species population model; Time delayed reaction diffusion equation; Travelling front; Uniqueness

Indexed keywords

BANACH SPACES; LINEAR EQUATIONS; SEMICONDUCTOR DOPING; TOPOLOGY; TURBULENT FLOW;

EID: 49749103184     PISSN: 13645021     EISSN: 14712946     Source Type: Journal    
DOI: 10.1098/rspa.2008.0011     Document Type: Article
Times cited : (25)

References (22)
  • 1
    • 33750189759 scopus 로고    scopus 로고
    • Traveling wave fronts for generalized Fisher equations with spatio-temporal delays
    • doi:10.1016/j.jde.2006.08.015
    • Ai, S. 2007 Traveling wave fronts for generalized Fisher equations with spatio-temporal delays. J. Differ. Equ. 232, 104-133. (doi:10.1016/j.jde.2006.08.015)
    • (2007) J. Differ. Equ , vol.232 , pp. 104-133
    • Ai, S.1
  • 4
    • 0001944424 scopus 로고
    • Run for your life. A note on the asymptotic speed of propagation of an epidemic
    • doi:10.1016/0022-0396(79)90080-9
    • Diekmann, O. 1979 Run for your life. A note on the asymptotic speed of propagation of an epidemic. J. Differ. Equ. 33, 58-73. (doi:10.1016/0022-0396(79)90080-9)
    • (1979) J. Differ. Equ , vol.33 , pp. 58-73
    • Diekmann, O.1
  • 5
    • 33745891805 scopus 로고    scopus 로고
    • Non-monotone travelling waves in a single species reaction-diffusion equation with delay
    • doi:10.1016/j.jde.2006.05.006
    • Faria, T. & Trofimchuk, S. 2006 Non-monotone travelling waves in a single species reaction-diffusion equation with delay. J. Differ. Equ. 228, 357-376. (doi:10.1016/j.jde.2006.05.006)
    • (2006) J. Differ. Equ , vol.228 , pp. 357-376
    • Faria, T.1    Trofimchuk, S.2
  • 6
    • 33745920917 scopus 로고    scopus 로고
    • Travelling waves for delayed reaction diffusion equations with global response
    • doi:10.1098/rspa.2005.1554
    • Faria, T., Huang, W. & Wu, J. 2006 Travelling waves for delayed reaction diffusion equations with global response. Proc. R. Soc. A 462, 229-261. (doi:10.1098/rspa.2005.1554)
    • (2006) Proc. R. Soc. A , vol.462 , pp. 229-261
    • Faria, T.1    Huang, W.2    Wu, J.3
  • 8
    • 84879144864 scopus 로고    scopus 로고
    • A note on global attractivity in models of hematopoiesis
    • doi:10.1007/BF02514684
    • Gopalsamy, K., Trofimchuk, S. & Bantsur, N. 1998 A note on global attractivity in models of hematopoiesis. Ukrain. Math. J. 50, 3-12. (doi:10.1007/BF02514684)
    • (1998) Ukrain. Math. J , vol.50 , pp. 3-12
    • Gopalsamy, K.1    Trofimchuk, S.2    Bantsur, N.3
  • 9
    • 33745885794 scopus 로고    scopus 로고
    • Non-locality of reaction-diffusion equations induced by delay: Biological modeling and nonlinear dynamics
    • doi:10.1023/B:JOTH. 0000047249.39572.6d
    • Gourley, S. A., So, J. W.-H. & Wu, J. H. 2004 Non-locality of reaction-diffusion equations induced by delay: biological modeling and nonlinear dynamics. J. Math. Sci. 124, 5119-5153. (doi:10.1023/B:JOTH. 0000047249.39572.6d)
    • (2004) J. Math. Sci , vol.124 , pp. 5119-5153
    • Gourley, S.A.1    So, J.W.-H.2    Wu, J.H.3
  • 10
    • 0035994837 scopus 로고    scopus 로고
    • Halanay inequality, Yorke 3/2 stability criterion, and differential equations with maxima
    • doi:10.2748/tmj/1113247567
    • Ivanov, A., Liz, E. & Trofimchuk, S. 2002 Halanay inequality, Yorke 3/2 stability criterion, and differential equations with maxima. Tohoku Math. J. 54, 277-295. (doi:10.2748/tmj/1113247567)
    • (2002) Tohoku Math. J , vol.54 , pp. 277-295
    • Ivanov, A.1    Liz, E.2    Trofimchuk, S.3
  • 11
    • 17744386691 scopus 로고    scopus 로고
    • Attractivity properties of infinite delay Mackey-Glass type equations
    • Liz, E., Martinez, C. & Trofimchuk, S. 2002 Attractivity properties of infinite delay Mackey-Glass type equations. Differ. Integral Equ. 15, 875-896.
    • (2002) Differ. Integral Equ , vol.15 , pp. 875-896
    • Liz, E.1    Martinez, C.2    Trofimchuk, S.3
  • 12
    • 17744367652 scopus 로고    scopus 로고
    • A global stability criterion for a family of delayed population models
    • Liz, E., Pinto, M., Tkachenko, V. & Trofimchuk, S. 2005 A global stability criterion for a family of delayed population models. Quart. Appl. Math. 63, 56-70.
    • (2005) Quart. Appl. Math , vol.63 , pp. 56-70
    • Liz, E.1    Pinto, M.2    Tkachenko, V.3    Trofimchuk, S.4
  • 13
    • 34247862261 scopus 로고    scopus 로고
    • Traveling waves for non-local delayed diffusion equations via auxiliary equations
    • doi:10.1016/j.jde.2007.03.014
    • Ma, S. 2007 Traveling waves for non-local delayed diffusion equations via auxiliary equations. J. Differ. Equ. 237, 259-277. (doi:10.1016/j.jde.2007.03.014)
    • (2007) J. Differ. Equ , vol.237 , pp. 259-277
    • Ma, S.1
  • 14
    • 0001935025 scopus 로고    scopus 로고
    • The Fredholm alternative for functional differential equations of mixed type
    • doi:10.1023/A:1021889401235
    • Mallet-Paret, J. 1999 The Fredholm alternative for functional differential equations of mixed type. J. Dyn. Differ. Equ. 11, 1-47. (doi:10.1023/A:1021889401235)
    • (1999) J. Dyn. Differ. Equ , vol.11 , pp. 1-47
    • Mallet-Paret, J.1
  • 15
    • 36348976487 scopus 로고    scopus 로고
    • Domain-decomposition method for the global dynamics of delay differential equations with unimodal feedback
    • doi: 10.1098/rspa.2007.1890
    • Rost, G. & Wu, J. 2007 Domain-decomposition method for the global dynamics of delay differential equations with unimodal feedback. Proc. R. Soc. A 463, 2655-2669. (doi: 10.1098/rspa.2007.1890)
    • (2007) Proc. R. Soc. A , vol.463 , pp. 2655-2669
    • Rost, G.1    Wu, J.2
  • 16
    • 0001219328 scopus 로고    scopus 로고
    • Dirichlet problem for the diffusive Nicholson's blowflies equation
    • doi:10.1006/jdeq.1998.3489
    • So, J. W.-H. & Yang, Y. 1998 Dirichlet problem for the diffusive Nicholson's blowflies equation. J. Differ. Equ. 150, 317-348. (doi:10.1006/jdeq.1998.3489)
    • (1998) J. Differ. Equ , vol.150 , pp. 317-348
    • So, J.W.-H.1    Yang, Y.2
  • 17
    • 32044440101 scopus 로고    scopus 로고
    • A reaction-diffusion model for a single species with age structure. I. Travelling wavefronts on unbounded domains
    • doi:10.1098/rspa.2001. 0789
    • So, J. W.-H., Wu, J. & Zou, X. 2001 A reaction-diffusion model for a single species with age structure. I. Travelling wavefronts on unbounded domains. Proc. R. Soc. A 457, 1841-1853. (doi:10.1098/rspa.2001. 0789)
    • (2001) Proc. R. Soc. A , vol.457 , pp. 1841-1853
    • So, J.W.-H.1    Wu, J.2    Zou, X.3
  • 18
    • 0008260279 scopus 로고
    • Asymptotic estimates of the solutions of nonlinear integral equations and asymptotic speeds for the spread of populations
    • Thieme, H. R. 1979 Asymptotic estimates of the solutions of nonlinear integral equations and asymptotic speeds for the spread of populations. J. Reine Angew. Math. 306, 94-121.
    • (1979) J. Reine Angew. Math , vol.306 , pp. 94-121
    • Thieme, H.R.1
  • 19
    • 0345116416 scopus 로고    scopus 로고
    • Asymptotic speeds of spread and traveling waves for integral equations and delayed reaction-diffusion models
    • doi:10.1016/S0022-0396(03)00175-X
    • Thieme, H. R. & Zhao, X.-Q. 2003 Asymptotic speeds of spread and traveling waves for integral equations and delayed reaction-diffusion models. J. Differ. Equ. 195, 430-470. (doi:10.1016/S0022-0396(03)00175-X)
    • (2003) J. Differ. Equ , vol.195 , pp. 430-470
    • Thieme, H.R.1    Zhao, X.-Q.2
  • 20
    • 41649111711 scopus 로고    scopus 로고
    • Trofimchuk, E. & Trofimchuk, S. 2008 Admissible wavefront speeds for a single species reaction -diffusion equation with delay. Discrete Contin. Dyn. Syst, A 20, 407-423.
    • Trofimchuk, E. & Trofimchuk, S. 2008 Admissible wavefront speeds for a single species reaction -diffusion equation with delay. Discrete Contin. Dyn. Syst, A 20, 407-423.
  • 21
    • 85020778668 scopus 로고    scopus 로고
    • Trofimchuk, E., Tkachenko, V. & Trofimchuk, S. 2007 Slowly oscillating wave solutions of a single species reaction-diffusion equation with delay. Oberwolfach Preprints Series: OWP 2007-12, see http://www.mfo.de/ publications/owp/2007/OWP2007_12.pdf.
    • Trofimchuk, E., Tkachenko, V. & Trofimchuk, S. 2007 Slowly oscillating wave solutions of a single species reaction-diffusion equation with delay. Oberwolfach Preprints Series: OWP 2007-12, see http://www.mfo.de/ publications/owp/2007/OWP2007_12.pdf.
  • 22
    • 0343717093 scopus 로고    scopus 로고
    • Traveling wave fronts of reaction-diffusion systems with delay
    • doi:10.1023/A: 1016690424892
    • Wu, J. & Zou, X. 2001 Traveling wave fronts of reaction-diffusion systems with delay. J. Dyn. Differ. Equ. 13, 651-687. (doi:10.1023/A: 1016690424892)
    • (2001) J. Dyn. Differ. Equ , vol.13 , pp. 651-687
    • Wu, J.1    Zou, X.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.