论文标题
中等相互作用的粒子系统的种群交叉扩散系统的严格推导
Rigorous derivation of population cross-diffusion systems from moderately interacting particle systems
论文作者
论文摘要
shigesada-kawasaki-teramoto类型的种群交叉扩散系统以平均场型限制得出，从随机，中等相互作用的多个粒子系统中，用于整个空间中多种种群。随机模型中的扩散项非线性地取决于个体之间的相互作用，而漂移项是环境电位的梯度。在第一步中，平均场极限会导致中间非局部模型。当相互作用电位接近Dirac Delta分布时，局部交叉扩散系统是在中等尺度的第二步中得出的。事实证明，对于足够小的初始数据，证明了对中间和局部扩散系统的强大解决方案的全球存在。此外，提出了粒子水平上的数值模拟。
Population cross-diffusion systems of Shigesada-Kawasaki-Teramoto type are derived in a mean-field-type limit from stochastic, moderately interacting many-particle systems for multiple population species in the whole space. The diffusion term in the stochastic model depends nonlinearly on the interactions between the individuals, and the drift term is the gradient of the environmental potential. In the first step, the mean-field limit leads to an intermediate nonlocal model. The local cross-diffusion system is derived in the second step in a moderate scaling regime, when the interaction potentials approach the Dirac delta distribution. The global existence of strong solutions to the intermediate and the local diffusion systems is proved for sufficiently small initial data. Furthermore, numerical simulations on the particle level are presented.
