Heat-content and diffusive leakage from material sets in the low-diffusivity limit *

Abstract We generalize leading-order asymptotics of a form the heat content submanifold (van den Berg & Gilkey 2015) to setting time-dependent diffusion processes in limit vanishing diffusivity. Such arise naturally when advection–diffusion are viewed Lagrangian coordinates. prove that as diffusivity ɛ goes zero, diffusive transport out material set S under time-dependent, mass-preserving equation with initial condition given by characteristic function 1 S , is $\sqrt{\varepsilon /\pi }\enspace \mathrm{d}\overline{A}(\partial S)+o(\sqrt{\varepsilon })$?> ε / π d A ¯ ( ∂ stretchy="false">) + o . The surface measure $\mathrm{d}\overline{A}$?> so-called geometry mixing introduced (Karrasch Keller 2020). apply our result characterisation coherent structures dynamical systems.