The heat equation with the dynamic boundary condition as a singular limit of problems degenerating at the boundary

2022/12/21 by Yoshikazu Giga, Giga, Yoshikazu, Michał Łasica +3 · 2 citations
Computer Science · Mathematics · #35K20 #49J45 #53C40 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #Differential Equations and Numerical Methods #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2212.11241

openalex publication_date 2022/12/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We derive the dynamic boundary condition for the heat equation as a limit of boundary layer problems. We study convergence of their weak and strong solutions as the width of the layer tends to zero. We also discuss Γ-convergence of the functionals generating these flows. Our analysis of strong solutions depends on a new version of the Reilly identity.

Cited by

• Mosco convergence framework for singular limits of gradient flows on Hilbert spaces with applications
• Asymptotic analysis of transmission problems with parameter-dependent Robin conditions

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