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This article is cited in 2 scientific papers (total in 2 papers)
MATHEMATICAL MODELING AND NUMERICAL SIMULATION
Large-time asymptotic solutions of the nonlocal Fisher–Kolmogorov–Petrovskii–Piskunov equation
E. A. Levchenkoa, A. Yu. Trifonovab, A. V. Shapovalovab a Laboratory of Mathematical Physics of Mathematical Physics Department, Tomsk Polytechnic University, 30 Lenin ave., Tomsk, 634050, Russia
b Theoretical Physics Department, Tomsk State University, 36 Lenin ave., Tomsk, 634050, Russia
Abstract:
Asymptotic solutions are constructed for the 1D nonlocal Fisher–Kolmogorov–Petrovskii–Piskunov equation. Such solutions allow to describe the quasi-steady-state patterns. Similar asymptotic solutions of the dynamical Einstein–Ehrenfest system for the 2D Fisher–Kolmogorov–Petrovskii–Piskunov equation are found. The solutions describe properties of 2D patterns localized on 1D manifolds.
Keywords:
nonlocal Fisher–Kolmogorov–Petrovskii–Piskunov equation, asymptotic solution, pattern formation, Einstein—Ehrenfest system.
Received: 30.05.2013 Revised: 03.07.2013
Citation:
E. A. Levchenko, A. Yu. Trifonov, A. V. Shapovalov, “Large-time asymptotic solutions of the nonlocal Fisher–Kolmogorov–Petrovskii–Piskunov equation”, Computer Research and Modeling, 5:4 (2013), 543–558
Linking options:
https://www.mathnet.ru/eng/crm416 https://www.mathnet.ru/eng/crm/v5/i4/p543
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