A strongly degenerate parabolic aggregation equation
A strongly degenerate parabolic aggregation equation
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一个强简并抛物线聚合方程
DOI：
10.4310/cms.2011.v9.n3.a4
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发表时间：
2010
期刊：
影响因子：
--
通讯作者：
K. Karlsen
中科院分区：
文献类型：
--
作者：
F. Betancourt;R. Burger;K. Karlsen
本文讨论了一维空间中的强退化对流扩散方程，其对流通量涉及到给定位置一侧总质量的非线性函数。这个方程可以理解为种群个体的聚集模型，其解表示其局部密度。聚集机制由一个考虑扩散的简并扩散项来平衡。在强退化情况下，非局部问题的解通常是不连续的，需要定义为满足熵条件的弱解。建立了非局部问题的有限差分格式，并证明了其收敛于唯一的熵解。该方案源于将单调方案的除法差用于基元的局部PDE。数值例子说明了非局部问题的熵解的性质，特别是聚集现象。
This paper is concerned with a strongly degenerate convection-diffusion equation in one space dimension whose convective flux involves a non-linear function of the total mass to one side of the given position. This equation can be understood as a model of aggregation of the individuals of a population with the solution representing their local density. The aggregation mechanism is balanced by a degenerate diffusion term accounting for dispersal. In the strongly degenerate case, solutions of the non-local problem are usually discontinuous and need to be defined as weak solutions satisfying an entropy condition. A finite difference scheme for the non-local problem is formulated and its convergence to the unique entropy solution is proved. The scheme emerges from taking divided differences of a monotone scheme for the local PDE for the primitive. Numerical examples illustrate the behaviour of entropy solutions of the non-local problem, in particular the aggregation phenomenon.
DOI：
10.1007/s00526-008-0200-7
发表时间：
2009-06-01
影响因子：
2.1
作者：
Blanchet, Adrien;Carrillo, Jose A.;Laurencot, Philippe
通讯作者：
Laurencot, Philippe