Geodesic
Error estimate for classical solutions to the heat equation in a moving thin domain and its limit equation
Tatsu-Hiko Miura1 orcid
1Hirosaki University, Japan
Interfaces and free boundaries, Tome 25 (2023) no. 4, pp. 633-670

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DOI

We consider the Neumann-type problem of the heat equation in a moving thin domain around a given closed moving hypersurface. The main result of this paper is an error estimate in the sup-norm for classical solutions to the thin domain problem and a limit equation on the moving hypersurface which appears in the thin-film limit of the heat equation. To prove the error estimate, we show a uniform a priori estimate for a classical solution to the thin domain problem based on the maximum principle. Moreover, we construct a suitable approximate solution to the thin domain problem from a classical solution to the limit equation based on an asymptotic expansion of the thin domain problem and apply the uniform a priori estimate to the difference of the approximate solution and a classical solution to the thin domain problem.
DOI : 10.4171/ifb/499
Classification : 35-XX
Mots-clés : Heat equation, moving thin domain, uniform a priori estimate

Tatsu-Hiko Miura  1

1 Hirosaki University, Japan 
Tatsu-Hiko Miura. Error estimate for classical solutions to the heat equation in a moving thin domain and its limit equation. Interfaces and free boundaries, Tome 25 (2023) no. 4, pp. 633-670. doi: 10.4171/ifb/499
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     journal = {Interfaces and free boundaries},
     pages = {633--670},
     year = {2023},
     volume = {25},
     number = {4},
     doi = {10.4171/ifb/499},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/499/}
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