Accelerated front propagation for monostable equations with nonlocal diffusion: multidimensional case

Finkelshtein D, Kondratiev Y, Tkachov P (2019)
Journal of Elliptic and Parabolic Equations 5(2): 423–471.

Zeitschriftenaufsatz | Veröffentlicht| Englisch
 
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Autor*in
Finkelshtein, Dmitri; Kondratiev, YuriUniBi; Tkachov, Pasha
Abstract / Bemerkung
We describe acceleration of the front propagation for solutions to a class of monostable nonlinear equations with a nonlocal diffusion in R-d, d >= 1. We show that the acceleration takes place if either the diffusion kernel or the initial condition has 'regular' heavy tails in R-d (in particular, decays slower than exponentially). Under general assumptions which can be verified for particular models, we present sharp estimates for the time-space zone which separates the region of convergence to the unstable zero solution with the region of convergence to the stable positive constant solution. We show the variety of different possible rates of the propagation starting from a little bit faster than a linear one up to the exponential rate. The paper generalizes to the case d > 1 our results for the case d = 1 obtained early in Finkelshtein and Tkachov (Appl Anal 98(4):756-780, 2019).
Stichworte
Nonlocal diffusion; Reaction-diffusion equation; Front propagation; Acceleration; Monostable equation; Nonlocal nonlinearity; Long-time; behavior; Integral equation
Erscheinungsjahr
2019
Zeitschriftentitel
Journal of Elliptic and Parabolic Equations
Band
5
Ausgabe
2
Seite(n)
423–471
ISSN
2296-9020
eISSN
2296-9039
Page URI
https://pub.uni-bielefeld.de/record/2939176

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Finkelshtein D, Kondratiev Y, Tkachov P. Accelerated front propagation for monostable equations with nonlocal diffusion: multidimensional case. Journal of Elliptic and Parabolic Equations. 2019;5(2):423–471.
Finkelshtein, D., Kondratiev, Y., & Tkachov, P. (2019). Accelerated front propagation for monostable equations with nonlocal diffusion: multidimensional case. Journal of Elliptic and Parabolic Equations, 5(2), 423–471. doi:10.1007/s41808-019-00045-w
Finkelshtein, D., Kondratiev, Y., and Tkachov, P. (2019). Accelerated front propagation for monostable equations with nonlocal diffusion: multidimensional case. Journal of Elliptic and Parabolic Equations 5, 423–471.
Finkelshtein, D., Kondratiev, Y., & Tkachov, P., 2019. Accelerated front propagation for monostable equations with nonlocal diffusion: multidimensional case. Journal of Elliptic and Parabolic Equations, 5(2), p 423–471.
D. Finkelshtein, Y. Kondratiev, and P. Tkachov, “Accelerated front propagation for monostable equations with nonlocal diffusion: multidimensional case”, Journal of Elliptic and Parabolic Equations, vol. 5, 2019, pp. 423–471.
Finkelshtein, D., Kondratiev, Y., Tkachov, P.: Accelerated front propagation for monostable equations with nonlocal diffusion: multidimensional case. Journal of Elliptic and Parabolic Equations. 5, 423–471 (2019).
Finkelshtein, Dmitri, Kondratiev, Yuri, and Tkachov, Pasha. “Accelerated front propagation for monostable equations with nonlocal diffusion: multidimensional case”. Journal of Elliptic and Parabolic Equations 5.2 (2019): 423–471.