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

@article{Schilling2021HeatcontentAD,
  title={Heat-content and diffusive leakage from material sets in the low-diffusivity limit},
  author={Nathanael Schilling and Daniel Karrasch and Oliver Junge},
  journal={Nonlinearity},
  year={2021},
  volume={34},
  pages={7303 - 7321}
}
We generalize leading-order asymptotics of a form of the heat content of a submanifold (van den Berg & Gilkey 2015) to the setting of time-dependent diffusion processes in the limit of vanishing diffusivity. Such diffusion processes arise naturally when advection–diffusion processes are viewed in Lagrangian coordinates. We prove that as diffusivity ɛ goes to zero, the diffusive transport out of a material set S under the time-dependent, mass-preserving advection–diffusion equation with initial… 
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