Pattern formation in terms of semiclassically limited distribution on lower dimensional manifolds for the nonlocal Fisher-Kolmogorov-Petrovskii-Piskunov equation

Результат исследований: Материалы для журналаСтатья

8 Цитирования (Scopus)

Выдержка

We have investigated the pattern formation in systems described by the nonlocal Fisher-Kolmogorov-Petrovskii-Piskunov equation for the cases where the dimension of the pattern concentration domain is lower than that of the domain of independent variables. We have obtained a system of integro-differential equations which describe the dynamics of the concentration domain and the semiclassically limited density distribution for a pattern in the class of trajectory concentrated functions. Also, asymptotic large time solutions have been obtained that describe the semiclassically limited distribution for a quasi-steady-state pattern on the concentration manifold. The approach is illustrated by an example for which the analytical solution is in good agreement with the results of numerical calculations.

Язык оригиналаАнглийский
Номер статьи025209
ЖурналJournal of Physics A: Mathematical and Theoretical
Том47
Номер выпуска2
DOI
СостояниеОпубликовано - 17 янв 2014

Отпечаток

Integrodifferential equations
Pattern Formation
Trajectories
Large Time Asymptotics
Integro-differential Equation
Numerical Calculation
quasi-steady states
Analytical Solution
Trajectory
density distribution
differential equations
trajectories

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Modelling and Simulation
  • Mathematical Physics
  • Physics and Astronomy(all)

Цитировать

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AU - Levchenko, Evgeniy Anatolievich

AU - Shapovalov, Aleksandr Vasilievich

AU - Trifonov, A. Yu

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