The well-posedness of a non-local advection-selection-mutation problem deriving from adaptive dynamics models is shown for a wide family of initial data. A particle method is then developed, in order to approximate the solution of such problem by a regularised sum of weighted Dirac masses whose characteristics solve a suitably defined ODE system. The convergence of the particle method over any finite interval is shown and an explicit rate of convergence is given. Furthermore, we investigate the asymptotic-preserving properties of the method in large times, providing sufficient conditions for it to hold true as well as examples and counter-examples. Finally, we illustrate the method in two cases taken from the literature.

翻译：本文证明了一类源自自适应动力学模型的非局部对流-选择-突变问题的适定性，适用于广泛的初始数据族。随后，我们发展了一种粒子方法，通过正则化的加权狄拉克质量之和来近似该问题的解，其中这些狄拉克质量的特性由适当定义的常微分方程系统决定。我们证明了粒子方法在任意有限区间上的收敛性，并给出了显式的收敛速率。此外，我们研究了该方法在大时间尺度下的渐近保持性质，提供了其成立的充分条件，以及正例和反例。最后，我们通过文献中的两个案例对该方法进行了说明。