Multi-parameter perturbations for the space-periodic heat equation

2023/09/14 by Маттео Далла Ріва, Paolo Luzzini, Riva, Matteo Dalla +5 · 1 citation
Computer Science · Engineering · Mathematics · #31B10 #35B10 #35K20 #45A05 #47H30 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Composite Material Mechanics #FOS: Mathematics #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.2309.07501

openalex publication_date 2023/09/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper is divided into three parts. The first part focuses on periodic layer heat potentials, demonstrating their smooth dependence on regular perturbations of the support of integration. In the second part, we present an application of the results from the first part. Specifically, we consider a transmission problem for the heat equation in a periodic two-phase composite material and we show that the solution depends smoothly on the shape of the transmission interface, boundary data, and conductivity parameters. Finally, in the last part of the paper, we fix all parameters except for the contrast parameter and outline a strategy to deduce an explicit expansion of the solution using a Neumann-type series.

Cited by

• Shape sensitivity analysis of the heat equation and the Dirichlet-to-Neumann map

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