论文标题
一类反应 - 辅助扩散方程的最佳初始基准
The optimal initial datum for a class of reaction-advection-diffusion equations
论文作者
论文摘要
我们考虑一个在有限域中具有漂移项的反应扩散模型。给定时间$ t，$我们证明了初始基准的存在和唯一性，该数据最大化了总质量$ \ textstyle {\int_Ωu（t，x）\ mathrm {d} x} $在存在的情况下。在人群动态环境中，该最佳初始基准可以理解为初始人口的最佳分布，在两种情况下，我们还将总质量$ t $比较总体$ t $。我们证明，足够大的对流的存在可以增强总质量。
We consider a reaction-diffusion model with a drift term in a bounded domain. Given a time $T,$ we prove the existence and uniqueness of an initial datum that maximizes the total mass $\textstyle{\int_Ωu(T,x)\mathrm{d}x}$ in the presence of an advection term. In a population dynamics context, this optimal initial datum can be understood as the best distribution of the initial population that leads to a maximal the total population at a prefixed time $T.$ We also compare the total masses at a time $T$ in two cases: depending on whether an advection term is present in the medium or not. We prove that the presence of a large enough advection enhances the total mass.
