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math.AP2021★ 2 cited
Heat-content and diffusive leakage from material sets in the low-diffusivity limit
Nathanael Schillling, Daniel Karrasch, Oliver Junge
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 limi…
math.AP2021★ 7 cited
A Lagrangian perspective on nonautonomous advection-diffusion processes in the low-diffusivity limit
Daniel Karrasch, Nathanael Schilling
We study mass preserving transport of passive tracers in the low-diffusivity limit using Lagrangian coordinates. Over finite-time intervals, the solution-operator of the nonautonom…
math.AP2020★ 1 cited
Short-time heat content asymptotics via the wave and eikonal equations
Nathanael Schilling
In this short paper, we derive an alternative proof for some known [van den Berg & Gilkey 2015] short-time asymptotics of the heat content in compact full-dimensional submanifolds…