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Volumn 238, Issue 1, 2007, Pages 153-200

Existence and stability of traveling wave fronts in reaction advection diffusion equations with nonlocal delay

Author keywords

Asymptotic stability; Bistable; Existence; Nonlocal delay; Reaction advection diffusion equation; Traveling wave front; Uniqueness

Indexed keywords


EID: 34249084413     PISSN: 00220396     EISSN: 10902732     Source Type: Journal    
DOI: 10.1016/j.jde.2007.03.025     Document Type: Article
Times cited : (184)

References (49)
  • 1
    • 22644451006 scopus 로고    scopus 로고
    • Traveling waves for a periodic bistable equation and a singular perturbation problem
    • Alikakos N.D., Bates P.W., and Chen X. Traveling waves for a periodic bistable equation and a singular perturbation problem. Trans. Amer. Math. Soc. 351 (1999) 2777-2805
    • (1999) Trans. Amer. Math. Soc. , vol.351 , pp. 2777-2805
    • Alikakos, N.D.1    Bates, P.W.2    Chen, X.3
  • 3
    • 0344578958 scopus 로고    scopus 로고
    • Monotone traveling fronts in age-structured reaction-diffusion model of a single species
    • Al-Omari J.F.M., and Gourley S.A. Monotone traveling fronts in age-structured reaction-diffusion model of a single species. J. Math. Biol. 45 (2002) 294-312
    • (2002) J. Math. Biol. , vol.45 , pp. 294-312
    • Al-Omari, J.F.M.1    Gourley, S.A.2
  • 4
    • 21144440167 scopus 로고    scopus 로고
    • A nonlocal reaction-diffusion model for a single species with stage structure and distributed maturation delay
    • Al-Omari J.F.M., and Gourley S.A. A nonlocal reaction-diffusion model for a single species with stage structure and distributed maturation delay. European J. Appl. Math. 16 (2005) 37-51
    • (2005) European J. Appl. Math. , vol.16 , pp. 37-51
    • Al-Omari, J.F.M.1    Gourley, S.A.2
  • 5
    • 34249042398 scopus 로고    scopus 로고
    • Monotone wave-fronts in a structured population model with distributed maturation delay
    • Al-Omari J.F.M., and Gourley S.A. Monotone wave-fronts in a structured population model with distributed maturation delay. IMA J. Appl. Math. 16 (2005) 1-22
    • (2005) IMA J. Appl. Math. , vol.16 , pp. 1-22
    • Al-Omari, J.F.M.1    Gourley, S.A.2
  • 7
    • 21244493574 scopus 로고    scopus 로고
    • The influence of advection on the propagation of fronts in reaction-diffusion equations
    • Nonlinear PDEs in Condensed Matter and Reactive Flows. Berestycki H., and Pomeau Y. (Eds), Kluwer, Dordrecht
    • Berestycki H. The influence of advection on the propagation of fronts in reaction-diffusion equations. In: Berestycki H., and Pomeau Y. (Eds). Nonlinear PDEs in Condensed Matter and Reactive Flows. NATO Sci. Ser. C vol. 569 (2003), Kluwer, Dordrecht
    • (2003) NATO Sci. Ser. C , vol.569
    • Berestycki, H.1
  • 8
    • 0346040342 scopus 로고    scopus 로고
    • Dynamics of a strongly nonlocal reaction-diffusion population model
    • Billingham J. Dynamics of a strongly nonlocal reaction-diffusion population model. Nonlinearity 17 (2004) 313-346
    • (2004) Nonlinearity , vol.17 , pp. 313-346
    • Billingham, J.1
  • 9
    • 0025545718 scopus 로고
    • Spatial structures and periodic travelling waves in an integro-differential reaction-diffusion population model
    • Britton N.F. Spatial structures and periodic travelling waves in an integro-differential reaction-diffusion population model. SIAM J. Appl. Math. 50 (1990) 1663-1688
    • (1990) SIAM J. Appl. Math. , vol.50 , pp. 1663-1688
    • Britton, N.F.1
  • 10
    • 30444442775 scopus 로고    scopus 로고
    • Reaction-Diffusion Systems: Front Propagation and Spatial Structures
    • pp. 187-210
    • Cencini M., Lopez C., and Vergni D. Reaction-Diffusion Systems: Front Propagation and Spatial Structures. Lecture Notes in Phys. vol. 636 (2003) pp. 187-210
    • (2003) Lecture Notes in Phys. , vol.636
    • Cencini, M.1    Lopez, C.2    Vergni, D.3
  • 11
  • 12
    • 0001249829 scopus 로고
    • Generation and propagation of interfaces in reaction-diffusion equations
    • Chen X. Generation and propagation of interfaces in reaction-diffusion equations. J. Differential Equations 96 (1992) 116-141
    • (1992) J. Differential Equations , vol.96 , pp. 116-141
    • Chen, X.1
  • 13
    • 0001203924 scopus 로고    scopus 로고
    • Existence, uniqueness, and asymptotic stability of travelling waves in nonlocal evolution equations
    • Chen X. Existence, uniqueness, and asymptotic stability of travelling waves in nonlocal evolution equations. Adv. Differential Equations 2 (1997) 125-160
    • (1997) Adv. Differential Equations , vol.2 , pp. 125-160
    • Chen, X.1
  • 14
    • 0037144960 scopus 로고    scopus 로고
    • Existence and asymptotic stability of travelling waves of discrete quasilinear monostable equations
    • Chen X., and Guo J.S. Existence and asymptotic stability of travelling waves of discrete quasilinear monostable equations. J. Differential Equations 184 (2002) 549-569
    • (2002) J. Differential Equations , vol.184 , pp. 549-569
    • Chen, X.1    Guo, J.S.2
  • 15
    • 0037792197 scopus 로고    scopus 로고
    • Uniqueness and existence of travelling waves of discrete quasilinear monostable dynamics
    • Chen X., and Guo J.S. Uniqueness and existence of travelling waves of discrete quasilinear monostable dynamics. Math. Ann. 326 (2003) 123-146
    • (2003) Math. Ann. , vol.326 , pp. 123-146
    • Chen, X.1    Guo, J.S.2
  • 17
    • 0003227862 scopus 로고
    • Abstract Evolution Equations, Periodic Problems and Applications
    • Longman Scientific Technical, Harlow
    • Daners D., and McLeod P.K. Abstract Evolution Equations, Periodic Problems and Applications. Pitman Res. Notes Math. Ser. vol. 279 (1992), Longman Scientific Technical, Harlow
    • (1992) Pitman Res. Notes Math. Ser. , vol.279
    • Daners, D.1    McLeod, P.K.2
  • 18
    • 84971116294 scopus 로고
    • Existence and uniqueness of traveling waves for a neutral network
    • Ermentrout B., and McLeod J.B. Existence and uniqueness of traveling waves for a neutral network. Proc. Roy. Soc. Edinburgh Ser. A 123 (1993) 461-478
    • (1993) Proc. Roy. Soc. Edinburgh Ser. A , vol.123 , pp. 461-478
    • Ermentrout, B.1    McLeod, J.B.2
  • 19
    • 84990617538 scopus 로고
    • Phase transitions and generalized motion by mean curvature
    • Evans L.C., Soner H.M., and Souganidis P.E. Phase transitions and generalized motion by mean curvature. Comm. Pure Appl. Math. 45 (1992) 1097-1123
    • (1992) Comm. Pure Appl. Math. , vol.45 , pp. 1097-1123
    • Evans, L.C.1    Soner, H.M.2    Souganidis, P.E.3
  • 20
    • 0017637590 scopus 로고
    • The approach of solutions of nonlinear diffusion equations to traveling wave solutions
    • Fife P.C., and McLeod J.B. The approach of solutions of nonlinear diffusion equations to traveling wave solutions. Arch. Ration. Mech. Anal. 65 (1977) 355-361
    • (1977) Arch. Ration. Mech. Anal. , vol.65 , pp. 355-361
    • Fife, P.C.1    McLeod, J.B.2
  • 21
    • 34249025810 scopus 로고    scopus 로고
    • B.H. Gilding, R. Kersner, Travelling Waves in Nonlinear Diffusion-Convection-Reaction, Memorandum n. 1585, University of Twente, 2001
  • 22
    • 0033752098 scopus 로고    scopus 로고
    • Travelling fronts in the diffusive Nicholson's blowflies equation with distributed delays
    • Gourley S.A. Travelling fronts in the diffusive Nicholson's blowflies equation with distributed delays. Math. Comput. Modelling 32 (2000) 843-853
    • (2000) Math. Comput. Modelling , vol.32 , pp. 843-853
    • Gourley, S.A.1
  • 23
    • 0035500330 scopus 로고    scopus 로고
    • Wave front solutions of a diffusive delay model for populations of daphnia maga
    • Gourley S.A. Wave front solutions of a diffusive delay model for populations of daphnia maga. Comput. Math. Appl. 42 (2001) 1421-1430
    • (2001) Comput. Math. Appl. , vol.42 , pp. 1421-1430
    • Gourley, S.A.1
  • 24
    • 1542616886 scopus 로고    scopus 로고
    • Wavefronts and global stability in a time-delayed population model with stage structure
    • Gourley S.A., and Kuang Y. Wavefronts and global stability in a time-delayed population model with stage structure. Proc. R. Soc. Lond. Ser. A 59 (2003) 1563-1579
    • (2003) Proc. R. Soc. Lond. Ser. A , vol.59 , pp. 1563-1579
    • Gourley, S.A.1    Kuang, Y.2
  • 25
    • 2442624461 scopus 로고    scopus 로고
    • Convergence and travelling fronts in functional differential equations with nonlocal terms: A competition model
    • Gourley S.A., and Ruan S. Convergence and travelling fronts in functional differential equations with nonlocal terms: A competition model. SIAM J. Math. Anal. 35 (2003) 806-822
    • (2003) SIAM J. Math. Anal. , vol.35 , pp. 806-822
    • Gourley, S.A.1    Ruan, S.2
  • 26
    • 33745885794 scopus 로고    scopus 로고
    • Non-locality of reaction-diffusion equations induced by delay: Biological modeling and nonlinear dynamics
    • Gourley S.A., So J.H.W., and Wu J. Non-locality of reaction-diffusion equations induced by delay: Biological modeling and nonlinear dynamics. J. Math. Sci. 124 (2004) 5119-5153
    • (2004) J. Math. Sci. , vol.124 , pp. 5119-5153
    • Gourley, S.A.1    So, J.H.W.2    Wu, J.3
  • 27
    • 84867929521 scopus 로고    scopus 로고
    • Travelling waves and numerical approximations in a reaction advection diffusion equation with nonlocal delayed effects
    • Liang D., and Wu J. Travelling waves and numerical approximations in a reaction advection diffusion equation with nonlocal delayed effects. J. Nonlinear Sci. 13 (2003) 289-310
    • (2003) J. Nonlinear Sci. , vol.13 , pp. 289-310
    • Liang, D.1    Wu, J.2
  • 28
    • 34249015773 scopus 로고    scopus 로고
    • S. Ma, J. Wu, Existence, uniqueness and asymptotic stability of traveling wavefronts in non-local delayed diffusion equation, J. Dynam. Differential Equations, in press
  • 29
    • 24644479145 scopus 로고    scopus 로고
    • Existence, uniqueness and stability of traveling waves in a discrete reaction-diffusion monostable equation with delay
    • Ma S., and Zou X. Existence, uniqueness and stability of traveling waves in a discrete reaction-diffusion monostable equation with delay. J. Differential Equations 217 (2005) 54-87
    • (2005) J. Differential Equations , vol.217 , pp. 54-87
    • Ma, S.1    Zou, X.2
  • 30
    • 15444367223 scopus 로고    scopus 로고
    • Propagation and its failure in a lattice delayed differential equation with global interaction
    • Ma S., and Zou X. Propagation and its failure in a lattice delayed differential equation with global interaction. J. Differential Equations 212 (2005) 129-190
    • (2005) J. Differential Equations , vol.212 , pp. 129-190
    • Ma, S.1    Zou, X.2
  • 31
    • 0003289006 scopus 로고
    • Time Lags in Biological Models
    • Springer, Berlin
    • MacDonald N. Time Lags in Biological Models. Lecture Notes in Biomathematics vol. 27 (1978), Springer, Berlin
    • (1978) Lecture Notes in Biomathematics , vol.27
    • MacDonald, N.1
  • 32
    • 0036054752 scopus 로고    scopus 로고
    • Travelling wavefronts in reaction-diffusion equations with convection effects and non-regular terms
    • Malaguti L., and Marcelli C. Travelling wavefronts in reaction-diffusion equations with convection effects and non-regular terms. Math. Nachr. 242 (2002) 148-164
    • (2002) Math. Nachr. , vol.242 , pp. 148-164
    • Malaguti, L.1    Marcelli, C.2
  • 33
    • 34248998844 scopus 로고    scopus 로고
    • L. Malaguti, C. Marcelli, The influence of convective effects on front propagation in certain diffusive models, in: V. Capasso (Ed.), Mathematical Modelling and Computing in Biology and Medicine, 5th ESMTB Conference, 2002, Esculapio, Bologna, 2003, pp. 362-367
  • 34
    • 34249063674 scopus 로고    scopus 로고
    • Front propagation in bistable reaction-diffusion-advection equations
    • Malaguti L., Marcelli C., and Matucci S. Front propagation in bistable reaction-diffusion-advection equations. Adv. Differential Equations 9 (2004) 1143-1166
    • (2004) Adv. Differential Equations , vol.9 , pp. 1143-1166
    • Malaguti, L.1    Marcelli, C.2    Matucci, S.3
  • 35
    • 84966246501 scopus 로고
    • Abstract functional differential equations and reaction-diffusion systems
    • Martin R.H., and Smith H.L. Abstract functional differential equations and reaction-diffusion systems. Trans. Amer. Math. Soc. 321 (1990) 1-44
    • (1990) Trans. Amer. Math. Soc. , vol.321 , pp. 1-44
    • Martin, R.H.1    Smith, H.L.2
  • 36
    • 24344466694 scopus 로고    scopus 로고
    • Existence and uniqueness of a wavefront in a delayed hyperbolic-parabolic model
    • Ou C., and Wu J. Existence and uniqueness of a wavefront in a delayed hyperbolic-parabolic model. Nonlinear Anal. 63 (2005) 364-387
    • (2005) Nonlinear Anal. , vol.63 , pp. 364-387
    • Ou, C.1    Wu, J.2
  • 37
    • 10044257560 scopus 로고    scopus 로고
    • Stability of steady states and existence of traveling waves in a vector disease model
    • Ruan S., and Xiao D. Stability of steady states and existence of traveling waves in a vector disease model. Proc. Roy. Soc. Edinburgh Ser. A 134 (2004) 991-1011
    • (2004) Proc. Roy. Soc. Edinburgh Ser. A , vol.134 , pp. 991-1011
    • Ruan, S.1    Xiao, D.2
  • 38
    • 0001584326 scopus 로고
    • Asymptotic behavior and travelling wave solutions for parabolic functional differential equations
    • Schaaf K.W. Asymptotic behavior and travelling wave solutions for parabolic functional differential equations. Trans. Amer. Math. Soc. 302 (1987) 587-615
    • (1987) Trans. Amer. Math. Soc. , vol.302 , pp. 587-615
    • Schaaf, K.W.1
  • 39
    • 0033589602 scopus 로고    scopus 로고
    • Traveling waves in time almost periodic structures governed by bistable nonlinearities. I. Stability and uniqueness
    • Shen W. Traveling waves in time almost periodic structures governed by bistable nonlinearities. I. Stability and uniqueness. J. Differential Equations 159 (1999) 1-54
    • (1999) J. Differential Equations , vol.159 , pp. 1-54
    • Shen, W.1
  • 40
    • 0033589576 scopus 로고    scopus 로고
    • Traveling waves in time almost periodic structures governed by bistable nonlinearities. II. Existence
    • Shen W. Traveling waves in time almost periodic structures governed by bistable nonlinearities. II. Existence. J. Differential Equations 159 (1999) 55-101
    • (1999) J. Differential Equations , vol.159 , pp. 55-101
    • Shen, W.1
  • 41
    • 0001676484 scopus 로고
    • Strongly order preserving semiflows generated by functional differential equations
    • Smith H.L., and Thieme H. Strongly order preserving semiflows generated by functional differential equations. J. Differential Equations 93 (1991) 332-363
    • (1991) J. Differential Equations , vol.93 , pp. 332-363
    • Smith, H.L.1    Thieme, H.2
  • 42
    • 0040807398 scopus 로고    scopus 로고
    • Global asymptotic stability of travelling waves in delayed reaction-diffusion equations
    • Smith H.L., and Zhao X.Q. Global asymptotic stability of travelling waves in delayed reaction-diffusion equations. SIAM J. Math. Anal. 31 (2000) 514-534
    • (2000) SIAM J. Math. Anal. , vol.31 , pp. 514-534
    • Smith, H.L.1    Zhao, X.Q.2
  • 43
    • 32044440101 scopus 로고    scopus 로고
    • A reaction-diffusion model for a single species with age structure. I, Travelling wavefronts on unbounded domains
    • So J.W.H., Wu J., and Zou X. A reaction-diffusion model for a single species with age structure. I, Travelling wavefronts on unbounded domains. Proc. R. Soc. Lond. Ser. A 457 (2003) 1841-1853
    • (2003) Proc. R. Soc. Lond. Ser. A , vol.457 , pp. 1841-1853
    • So, J.W.H.1    Wu, J.2    Zou, X.3
  • 44
    • 0001412912 scopus 로고
    • Travelling Wave Solutions of Parabolic Systems
    • Amer. Math. Soc., Providence, RI
    • Volpert A.I., Volpert V.A., and Volpert V.A. Travelling Wave Solutions of Parabolic Systems. Transl. Math. Monogr. vol. 140 (1994), Amer. Math. Soc., Providence, RI
    • (1994) Transl. Math. Monogr. , vol.140
    • Volpert, A.I.1    Volpert, V.A.2    Volpert, V.A.3
  • 45
    • 0038432007 scopus 로고
    • Remarques sur la note de M. Régnier et Mlle. Lambin (Étude d'un cas d'antagonisme microbien)
    • Volterra V. Remarques sur la note de M. Régnier et Mlle. Lambin (Étude d'un cas d'antagonisme microbien). C. R. Acad. Sci. 199 (1934) 1684-1686
    • (1934) C. R. Acad. Sci. , vol.199 , pp. 1684-1686
    • Volterra, V.1
  • 46
    • 32044459052 scopus 로고    scopus 로고
    • Travelling wave fronts of reaction-diffusion systems with spatio-temporal delays
    • Wang Z.C., Li W.T., and Ruan S. Travelling wave fronts of reaction-diffusion systems with spatio-temporal delays. J. Differential Equations 222 (2006) 185-232
    • (2006) J. Differential Equations , vol.222 , pp. 185-232
    • Wang, Z.C.1    Li, W.T.2    Ruan, S.3
  • 47
    • 34249031297 scopus 로고    scopus 로고
    • Z.C. Wang, W.T. Li, S. Ruan, Existence, uniqueness and asymptotic stability of travelling wave fronts in nonlocal reaction-diffusion equations with delay, 2005, submitted for publication
  • 48
    • 0010750897 scopus 로고    scopus 로고
    • Introduction to Neural Dynamics and Signal Transmission Delay
    • de Gruyter, Berlin
    • Wu J. Introduction to Neural Dynamics and Signal Transmission Delay. de Gruyter Ser. Nonlinear Anal. Appl. (2002), de Gruyter, Berlin
    • (2002) de Gruyter Ser. Nonlinear Anal. Appl.
    • Wu, J.1
  • 49
    • 0037106115 scopus 로고    scopus 로고
    • Delay induced traveling wave fronts in reaction diffusion equations of KPP-Fisher type
    • Zou X. Delay induced traveling wave fronts in reaction diffusion equations of KPP-Fisher type. J. Comput. Appl. Math. 146 (2002) 309-321
    • (2002) J. Comput. Appl. Math. , vol.146 , pp. 309-321
    • Zou, X.1


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