2022/08/02 by Tatsu‐Hiko Miura, Miura, Tatsu-Hiko
Computer Science · Mathematics · #35R01 #35R37 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #FOS: Mathematics #Numerical methods in inverse problems #Primary: 35K05 #Secondary: 35B25
paper · pdf · doi:10.48550/arxiv.2208.01306
openalex publication_date 2022/08/02 · openalex created_date 2022/08/04 · openalex updated_date 2026/07/28
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.