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arXiv · 2202.10714

The optimal initial datum for a class of reaction-advection-diffusion equations

Omar Abdul Halim·Mohammad El Smaily
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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 $\textstyle{\int_\Omega u(T,x)\mathrm{d}x}$ 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.

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Omar Abdul Halim, Mohammad El Smaily. 2022-02-22. The optimal initial datum for a class of reaction-advection-diffusion equations. https://arxiv.org/abs/2202.10714

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