Nonmonotone travelling waves in a single species reaction–diffusion equation with delay

Journal of Differential Equations - Tập 228 - Trang 357-376 - 2006
Teresa Faria1, Sergei Trofimchuk2
1Departamento de Matemática, Faculdade de Ciências/CMAF, Universidade Lisboa, 1749-016 Lisboa, Portugal
2Instituto de Matemática y Fisica, Universidad de Talca, Casilla 747, Talca, Chile

Tài liệu tham khảo

Al-Omari, 2002, Monotone travelling fronts in an age-structured reaction–diffusion model of a single species, J. Math. Biol., 45, 294, 10.1007/s002850200159 Ambrosetti, 1993 Chicone, 1999 Diekmann, 1995 Engel, 1999 Faria, 2006, Traveling waves for delayed reaction–diffusion equations with nonlocal response, Proc. Roy. Soc. London Sect. A, 462, 229, 10.1098/rspa.2005.1554 Faria, 2005, On a generalized Yorke condition for scalar delayed population models, Discrete Contin. Dyn. Syst., 12, 481, 10.3934/dcds.2005.12.481 T. Faria, S. Trofimchuk, Positive heteroclinics and traveling waves for scalar population models with a single delay, Appl. Math. Comput., in press Gourley, 2000, Travelling fronts in the diffusive Nicholson's blowflies equation with distributed delays, Math. Comput. Modelling, 32, 843, 10.1016/S0895-7177(00)00175-8 Gourley, 2003, Wavefronts and global stability in time-delayed population model with stage structure, Proc. Roy. Soc. London Sect. A, 459, 1563, 10.1098/rspa.2002.1094 Gourley, 2000, Dynamics of the diffusive Nicholson's blowflies equation with distributed delay, Proc. Roy. Soc. Edinburgh Sect. A, 130, 1275, 10.1017/S0308210500000688 Gourley, 2004, Non-locality of reaction–diffusion equations induced by delay: Biological modeling and nonlinear dynamics, J. Math. Sci., 124, 5119, 10.1023/B:JOTH.0000047249.39572.6d Gurney, 1998 Győri, 1991 Győri, 2002, On the existence of rapidly oscillatory solutions in the Nicholson blowflies equation, Nonlinear Anal., 48, 1033, 10.1016/S0362-546X(00)00232-7 Hale, 1988 Hale, 1993 Hupkes, 2005, Analysis of Newton's method to compute travelling waves in discrete media, J. Dynam. Differential Equations, 17, 523, 10.1007/s10884-005-5809-z H.J. Hupkes, S.M. Verduyn Lunel, Analysis of Newton's method to compute travelling wave solutions to lattice differential equations, Technical report 2003-09, Mathematical Institute, Leiden Liang, 2003, Travelling waves and numerical approximations in a reaction advection diffusion equation with nonlocal delayed effects, J. Nonlinear Sci., 13, 289, 10.1007/s00332-003-0524-6 Liz, 2005, A global stability criterion for a family of delayed population models, Quart. Appl. Math., 63, 56, 10.1090/S0033-569X-05-00951-3 Liz, 2003, A global stability criterion for scalar functional differential equations, SIAM J. Math. Anal., 35, 596, 10.1137/S0036141001399222 Ma, 2001, Traveling wavefronts for delayed reaction–diffusion systems via a fixed point theorem, J. Differential Equations, 171, 294, 10.1006/jdeq.2000.3846 Mallet-Paret, 1999, The Fredholm alternative for functional differential equations of mixed type, J. Dynam. Differential Equations, 11, 1, 10.1023/A:1021889401235 Mei, 2004, Asymptotic stability of travelling waves for Nicholson's blowflies equation with diffusion, Proc. Roy. Soc. Edinburgh Sect. A, 134, 579, 10.1017/S0308210500003358 Smith, 1991, Strongly order preserving semiflows generated by functional differential equations, J. Differential Equations, 93, 332, 10.1016/0022-0396(91)90016-3 Smith, 2000, Global asymptotic stability of traveling waves in delayed reaction–diffusion equations, SIAM J. Math. Anal., 31, 514, 10.1137/S0036141098346785 Smoller, 1980 So, 2001, A reaction–diffusion model for a single species with age structure I. Traveling wavefronts on unbounded domains, Proc. Roy. Soc. London Sect. A, 457, 1841, 10.1098/rspa.2001.0789 So, 1998, Dirichlet problem for the diffusive Nicholson's blowflies equation, J. Differential Equations, 150, 317, 10.1006/jdeq.1998.3489 So, 2001, Traveling waves for the diffusive Nicholson's blowflies equation, Appl. Math. Comput., 122, 385, 10.1016/S0096-3003(00)00055-2 Wu, 2001, Traveling wave fronts of reaction–diffusion systems with delay, J. Dynam. Differential Equation, 13, 651, 10.1023/A:1016690424892