On the minimal speed of traveling waves for a nonlocal delayed reaction–diffusion equation

Nonlinear Oscillations - Tập 13 - Trang 1-9 - 2010
M. Aguerrea1, G. Valenzuela1
1Instituto de Matemática y Física, Universidad de Talca, Talca, Chile

Tóm tắt

In this note, we give constructive upper and lower bounds for the minimal speed of propagation of traveling waves for a nonlocal delayed reaction–diffusion equation.

Tài liệu tham khảo

S. A. Gourley, J. So, and J. Wu, “Nonlocality of reaction–diffusion equations induced by delay: biological modeling and nonlinear dynamics,” J. Math. Sci., 124, 5119–5153 (2004). W.-T. Li, S. Ruan, and Z.-C.Wang, “On the diffusive Nicholson’s blowflies equation with nonlocal delay,” J. Nonlinear Sci., 17, No. 6, 505–525 (2007). J. So, J. Wu, and X. Zou, “A reaction–diffusion model for a single species with age structure. I. Travelling wavefronts on unbounded domains,” Proc. Roy. Soc. A, 457, 1841–1853 (2001). E. Trofimchuk, P. Alvarado, and S. Trofimchuk, On the Geometry of Wave Solutions of a Delayed Reaction–Diffusion Equation, e-print: arXiv:math/0611753v2 [math. DS] (2008). Z.-C. Wang, W.-T. Li, and S. Ruan, “Traveling fronts in monostable equations with nonlocal delayed effects,” J. Dyn. Diff. Equat., 20, 573–607 (2008). S. Ma, “Traveling waves for nonlocal delayed diffusion equations via auxiliary equations,” J. Different. Equat., 237, 259–277 (2007). K.W. Schaaf, “Asymptotic behavior and traveling wave solutions for parabolic functional differential equations,” Trans. Amer. Math. Soc., 302, 587–615 (1987). E. Trofimchuk and S. Trofimchuk, “Admissible wavefront speeds for a single species reaction–diffusion equation with delay,” Discr. Contin. Dyn. Syst. A, 20, 407–423 (2008). J. Wu, D. Wei, and M. Mei, “Analysis on the critical speed of traveling waves,” Appl. Math. Lett., 20, 712–718 (2007). M. Aguerrea, S. Trofimchuk, and G. Valenzuela, “Uniqueness of fast travelling fronts in a single species reaction–diffusion equation with delay,” Proc. Roy. Soc. A, 464 (2008).