On an elastic model arising from volcanology: an analysis of the direct and inverse problem
Analysis of PDEs
2020-09-16 v2
Abstract
In this paper we investigate a mathematical model arising from volcanology describing surface deformation effects generated by a magma chamber embedded into Earth's interior and exerting on it a uniform hydrostatic pressure. The modeling assumptions translate mathematically into a Neumann boundary value problem for the classical Lam\'e system in a half-space with an embedded pressurized cavity. We establish well-posedness of the problem in suitable weighted Sobolev spaces and analyse the inverse problem of determining the pressurized cavity from partial measurements of the displacement field proving uniqueness and stability estimates.
Keywords
Cite
@article{arxiv.1705.11099,
title = {On an elastic model arising from volcanology: an analysis of the direct and inverse problem},
author = {Andrea Aspri and Elena Beretta and Edi Rosset},
journal= {arXiv preprint arXiv:1705.11099},
year = {2020}
}