The optimal initial datum for a class of reaction–advection–diffusion equations. (August 2022) - Abdul Halim, Omar; El Smaily, Mohammad
Abstract: 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 ∫ Ω u ( T, x ) 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.