Abstract
Asymptotic solutions of the nonlocal, one-dimensional Fisher–Kolmogorov–Petrovskii–Piskunov equation with fractional derivatives in the diffusion operator are constructed. The fractional derivative is defined in accordance with the approaches of Weyl, Grünwald–Letnilkov, and Liouville. Asymptotic solutions are constructed in a class of functions that are a perturbation of the found exact quasistationary solution and tend at large times to this quasistationary solution. It is shown that the presence of fractional derivatives leads to drift of the center of mass of the initial distribution and breaks its symmetry.
| Original language | English |
|---|---|
| Article number | A019 |
| Pages (from-to) | 399-409 |
| Number of pages | 11 |
| Journal | Russian Physics Journal |
| Volume | 58 |
| Issue number | 3 |
| DOIs | |
| Publication status | Published - 17 Jul 2015 |
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Keywords
- Anomalous diffusion
- Asymmetric solutions
- Nonlocal Fisher–KPP equation
ASJC Scopus subject areas
- Physics and Astronomy(all)
Cite this
Elementary particle physics and field theory : Asymptotic behavior of the one-dimensional fisher–kolmogorov–petrovskii–piskunov equation with anomalouos diffusion. / Prozorov, Alexander Andreevich; Trifonov, A. Yu; Shapovalov, Aleksandr Vasilievich.
In: Russian Physics Journal, Vol. 58, No. 3, A019, 17.07.2015, p. 399-409.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Elementary particle physics and field theory
T2 - Asymptotic behavior of the one-dimensional fisher–kolmogorov–petrovskii–piskunov equation with anomalouos diffusion
AU - Prozorov, Alexander Andreevich
AU - Trifonov, A. Yu
AU - Shapovalov, Aleksandr Vasilievich
PY - 2015/7/17
Y1 - 2015/7/17
N2 - Asymptotic solutions of the nonlocal, one-dimensional Fisher–Kolmogorov–Petrovskii–Piskunov equation with fractional derivatives in the diffusion operator are constructed. The fractional derivative is defined in accordance with the approaches of Weyl, Grünwald–Letnilkov, and Liouville. Asymptotic solutions are constructed in a class of functions that are a perturbation of the found exact quasistationary solution and tend at large times to this quasistationary solution. It is shown that the presence of fractional derivatives leads to drift of the center of mass of the initial distribution and breaks its symmetry.
AB - Asymptotic solutions of the nonlocal, one-dimensional Fisher–Kolmogorov–Petrovskii–Piskunov equation with fractional derivatives in the diffusion operator are constructed. The fractional derivative is defined in accordance with the approaches of Weyl, Grünwald–Letnilkov, and Liouville. Asymptotic solutions are constructed in a class of functions that are a perturbation of the found exact quasistationary solution and tend at large times to this quasistationary solution. It is shown that the presence of fractional derivatives leads to drift of the center of mass of the initial distribution and breaks its symmetry.
KW - Anomalous diffusion
KW - Asymmetric solutions
KW - Nonlocal Fisher–KPP equation
UR - http://www.scopus.com/inward/record.url?scp=84937046732&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84937046732&partnerID=8YFLogxK
U2 - 10.1007/s11182-015-0514-9
DO - 10.1007/s11182-015-0514-9
M3 - Article
AN - SCOPUS:84943360805
VL - 58
SP - 399
EP - 409
JO - Russian Physics Journal
JF - Russian Physics Journal
SN - 1064-8887
IS - 3
M1 - A019
ER -