Stability of non-monotone critical traveling waves for reaction–diffusion equations with time-delay
Tài liệu tham khảo
Aguerrea, 2012, On uniqueness of semi-wavefronts, Math. Ann., 354, 73, 10.1007/s00208-011-0722-8
Boese, 1987, Some stability charts and stability conditions for a class of difference-differential equations, ZAMM Z. Angew. Math. Mech., 67, 56
Fang, 2010, Existence and uniqueness of traveling waves for non-monotone integral equations with in applications, J. Differential Equations, 248, 2199, 10.1016/j.jde.2010.01.009
Faria, 2006, Traveling waves for delayed reaction–diffusion equations with global response, Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci., 462, 229, 10.1098/rspa.2005.1554
Faria, 2006, Nonmonotone traveling waves in single species reaction–diffusion equation with delay, J. Differential Equations, 228, 357, 10.1016/j.jde.2006.05.006
Faria, 2007, Positive heteroclinics and traveling waves for scalar population models with a single delay, Appl. Math. Comput., 185, 594
Gomez, 2014, Global continuation of monotone wavefronts, J. Lond. Math. Soc., 89, 47, 10.1112/jlms/jdt050
Gourley, 2003, Non-locality of reaction–diffusion equations induced by delay: biological modeling and nonlinear dynamics, 84
Gourley, 2006, Delayed nonlocal diffusive system in biological invasion and disease spread, vol. 48, 137
Huang, 2012, Planar traveling waves for nonlocal dispersal equation with monostable nonlinearity, Discrete Contin. Dyn. Syst. Ser. A, 32, 3621, 10.3934/dcds.2012.32.3621
R. Huang, M. Mei, K.-J. Zhang, Q.-F. Zhang, Stability of oscillating wavefronts for time-delayed nonlocal dispersal equations, preprint, 2014.
Liang, 2003, Traveling waves and numerical approximations in a reaction–diffusion equation with nonlocal delayed effect, J. Nonlinear Sci., 13, 289, 10.1007/s00332-003-0524-6
Lin, 2014, Exponential stability of non-monotone traveling waves for Nicholson's blowflies equation, SIAM J. Math. Anal., 46, 1053, 10.1137/120904391
Ma, 2007, Traveling waves for non-local delayed diffusion equations via auxiliary equations, J. Differential Equations, 237, 259, 10.1016/j.jde.2007.03.014
Matsumura, 1997, Nonlinear stability of viscous shock profile for a non-convex system of viscoelasticity, Osaka J. Math., 34, 589
Mei, 2009, Traveling wavefronts for time-delayed reaction–diffusion equation: (I) local nonlinearity, J. Differential Equations, 247, 495, 10.1016/j.jde.2008.12.026
Mei, 2009, Traveling wavefronts for time-delayed reaction–diffusion equation: (II) nonlocal nonlinearity, J. Differential Equations, 247, 511, 10.1016/j.jde.2008.12.020
Mei, 2010, Global stability of monostable traveling waves for nonlocal time-delayed reaction–diffusion equations, SIAM J. Math. Anal., 42, 2762, 10.1137/090776342
Mei, 2008, Stability of strong traveling waves for a nonlocal time-delayed reaction–diffusion equation, Proc. Roy. Soc. Edinburgh Sect. A, 138, 551, 10.1017/S0308210506000333
Mei, 2004, Asymptotic stability of traveling waves for the Nicholson's blowflies equation with diffusion, Proc. Roy. Soc. Edinburgh Sect. A, 134, 579, 10.1017/S0308210500003358
Mei, 2011, Remark on stability of traveling waves for nonlocal Fisher–KPP equations, Int. J. Numer. Anal. Model. Ser. B, 2, 379
Moet, 1979, A note on asymptotic behavior of solutions of the KPP equation, SIAM J. Math. Anal., 10, 728, 10.1137/0510067
Nishihara, 2000, Lp-convergence rate to nonlinear diffusion waves for p-system with damping, J. Differential Equations, 161, 191, 10.1006/jdeq.1999.3703
Radu, 2010, Decay estimates for wave equations with variable coefficients, Trans. Amer. Math. Soc., 362, 2279, 10.1090/S0002-9947-09-04742-4
Rothe, 1978, Convergence to travelling fronts in semilinear parabolic equations, Proc. Roy. Soc. Edinburgh Sect. A, 80, 213, 10.1017/S0308210500010258
Sherratt, 1998, On the transition from initial data to travelling waves in the Fisher–KPP equation, Dyn. Stab. Syst., 13, 167, 10.1080/02681119808806258
Smith, 2011, An Introduction to Delay Differential Equations with Applications to the Life Sciences, vol. 57
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
Tang, 1998, Oscillation of delay differential equations with variable coefficients, J. Math. Anal. Appl., 217, 32, 10.1006/jmaa.1997.5693
Todorova, 2007, Nonlinear dissipative wave equations with potential, vol. 426, 317
Trofimchuk, 2008, Admissible wavefront speeds for a single species reaction–diffusion equation with delay, Discrete Contin. Dyn. Syst. Ser. A, 20, 407, 10.3934/dcds.2008.20.407
Trofimchuk, 2008, Slowly oscillating wave solutions of a single species reaction–diffusion equation with delay, J. Differential Equations, 245, 2307, 10.1016/j.jde.2008.06.023
van Saarloos, 2003, Front propagation into unstable states, Phys. Rep., 386, 29, 10.1016/j.physrep.2003.08.001
Wang, 2007, Existence and stability of planar diffusion waves for 2-D Euler equations with damping, J. Differential Equations, 242, 40, 10.1016/j.jde.2007.07.002
Zhao, 2003