Publication Cover
Applicable Analysis
An International Journal
Volume 99, 2020 - Issue 13
204
Views
3
CrossRef citations to date
0
Altmetric
Articles

Speed of wave propagation for a nonlocal reaction–diffusion equation

&
Pages 2307-2321 | Received 06 Oct 2018, Accepted 11 Dec 2018, Published online: 18 Dec 2018

References

  • Ermentrout B, McLeod JB. Existence and uniqueness of traveling waves for a neural network. Proc R Soc Edinburgh. 1993;123A:461–478. doi: 10.1017/S030821050002583X
  • Modolo J, Bhattacharya B, Edwards R, et al. Using a virtual cortical module implementing a neural field model to modulate brain rhythms in Parkinsons disease. Front Neurosci. 2010;4:45. article
  • Hadeler KP, Rothe F. Travelling fronts in nonlinear diffusion equations. J Math Biol. 1975;2:251–263. doi: 10.1007/BF00277154
  • Volpert Vit A, Volpert Vl A. Propagation velocity estimation for condensed phase combustion. SIAM J Appl Math. 1991;51(4):1074–1089. doi: 10.1137/0151054
  • Volpert V. Elliptic partial differential equations. Vol. 2, Reaction–diffusion equations. Basel, Birkhäuser, 2014.
  • Galochkina T, Bouchnita A, Kurbatova P, et al. Reaction–diffusion waves of blood coagulation. Math Biosci. 2017;288:130–139. doi: 10.1016/j.mbs.2017.03.008
  • Coville J, Dupaigne L. Propagation speed of travelling fronts in non local reaction–diffusion equations. Nonlinear Anal. 2005;60(5):797–819. doi: 10.1016/j.na.2003.10.030
  • Ducrot A, Marion M, Volpert V. Spectrum of some integro-differential operators and stability of travelling waves. Nonlinear Anal. 2011;74(13):4455–4473. doi: 10.1016/j.na.2011.04.009
  • Bessonov N, Beuter A, Trofimchuk S, et al. Estimate of the travelling wave speed for an integro-differential equation. Appl Math Lett. 2019; 88:103–110.
  • Benguria RD, Depassier MC. Variational characterization of the speed of propagation of fronts for the nonlinear diffusion equation. Commun Math Phys. 1996;175:221–227. doi: 10.1007/BF02101631
  • Heinze S, Papanicolaou G, Stevens A. Variational principles for propagation speeds in inhomogeneous media. SIAM J Appl Math. 2001;62(1):129–148. doi: 10.1137/S0036139999361148
  • Smith HL. Monotone dynamical systems: an introduction to the theory of competitive and cooperative systems. 41. Providence, RI, AMS, 1995. Mathematical Surveys and Monographs.
  • Martin Jr RH, Smith HL. Abstract functional–differential equations and reaction diffusion systems. Trans Am Math Soc. 1990;321:1–44.
  • Wu J. Theory and applications of partial functional differential equations. 119. New York, Springer, 1996. Applied Math. Sci.
  • Chen X. Existence, uniqueness, and asymptotic stability of travelling waves in nonlocal evolution equations. Adv Differ Equ. 1997;2:125–160.
  • Apreutesei N, Volpert V. Existence of travelling waves for a class of integro-differential equations from population dynamics. Int Electron J Pure Appl Math. 2012;5(2):53–67.
  • Ma S, Wu J. Existence, uniqueness and asymptotic stability of traveling wavefronts in a non-local delayed diffusion equation. J Dyn Differ Equ. 2007;19(2):391–436. doi: 10.1007/s10884-006-9065-7

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.