Dynamic linear equations in the presence of small perturbations of an interface
Year: 2026
Type: preprint
Abstract: We consider solutions to the initial boundary value problems for both heat and wave equations in two dimensions. In this paper, we aim to advance the development of high-order terms in the asymptotic expansions of current boundary perturbations caused by small perturbations of the shape of a $C^2$-boundary inhomogeneity. Our derivations are rigorously derived by the field expansion (FE) method (formal derivation) and proved by layer potential techniques. It extends those already derived for small-volume inhomogeneities to develop efficient algorithms for determining certain properties of the shape of an inhomogeneity based on boundary measurements.
Source: arXiv (Cornell University)
Authors: Daveau, Christian, Khelifi, Abdessatar
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225831982
Cites:
Cited by:
Related to: