Geodesic
Zero width limit of the heat equation on moving thin domains
Tatsu-Hiko Miura1 orcid
1University of Tokyo, Japan
Interfaces and free boundaries, Tome 19 (2017) no. 1, pp. 31-77

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DOI

We study the behavior of a variational solution to the Neumann type problem of the heat equation on a moving thin domain Ωε​(t) that converges to an evolving surface Γ(t) as the width of Ωε​(t) goes to zero. We show that, under suitable assumptions, the average in the normal direction of Γ(t) of a variational solution to the heat equation converges weakly in a function space on Γ(t) as the width of Ωε​(t) goes to zero, and that the limit is a unique variational solution to a limit equation on Γ(t), which is a new type of linear diffusion equation involving the mean curvature and the normal velocity of Γ(t). We also estimate the difference between variational solutions to the heat equation on Ωε​(t) and the limit equation on Γ(t).
DOI : 10.4171/ifb/376
Classification : 35-XX
Mots-clés : Heat equation, moving thin domains, evolving surfaces

Tatsu-Hiko Miura  1

1 University of Tokyo, Japan 
Tatsu-Hiko Miura. Zero width limit of the heat equation on moving thin domains. Interfaces and free boundaries, Tome 19 (2017) no. 1, pp. 31-77. doi: 10.4171/ifb/376
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     year = {2017},
     volume = {19},
     number = {1},
     doi = {10.4171/ifb/376},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/376/}
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