低维流形上非局部Fisher-Kolmogorov-Petrovskii-Piskunov方程半经典极限分布的斑图形成
Pattern formation in terms of semiclassically limited distribution on lower-dimensional manifolds for nonlocal Fisher--Kolmogorov--Petrovskii--Piskunov equation
摘要：
本文研究了由非局部Fisher-Kolmogorov-Petrovskii-Piskunov方程描述的系统中的斑图形成，其中斑图集中区的维数小于自变量空间的维数。我们得到了一个系统的积分微分方程描述的动力学的浓度区和半经典有限分布的一类轨迹集中的功能模式。此外，已获得的渐近大时间的解决方案，描述了半经典有限分布的准稳态模式的浓度歧管。通过一个实例说明了这种方法，其中的解析解与数值模拟的预测是吻合得很好。
英文摘要：
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 area is less than that of independent variables space. We have obtained a system of integro-differential equations which describe the dynamics of the concentration area and the semiclassically limited distribution of a pattern in the class of trajectory concentrated functions. Also, asymptotic large-time solutions have been obtained that describe the semiclassically limited distribution of 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 prediction of a numerical simulation.
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