On an elastic model arising from volcanology: An analysis of the direct and inverse problem

A. Aspri, E. Beretta, E. Rosset

Research output: Contribution to journalArticle

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 Lamé 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.

Original languageEnglish (US)
Pages (from-to)6400-6423
Number of pages24
JournalJournal of Differential Equations
Volume265
Issue number12
DOIs
StatePublished - Dec 15 2018

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Keywords

  • Half-space
  • Inverse problem
  • Lamé system
  • Neumann problem
  • Stability estimates
  • Weighted Sobolev spaces

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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