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.

On an elastic model arising from volcanology : An analysis of the direct and inverse problem / A. Aspri, E. Beretta, E. Rosset. - In: JOURNAL OF DIFFERENTIAL EQUATIONS. - ISSN 0022-0396. - 265:12(2018), pp. 6400-6423. [10.1016/j.jde.2018.07.031]

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

A. Aspri
Primo
;
2018

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.
Half-space; Inverse problem; Lamé system; Neumann problem; Stability estimates; Weighted Sobolev spaces
Settore MAT/05 - Analisi Matematica
Article (author)
File in questo prodotto:
File Dimensione Formato  
3.Aspri_JDE18.pdf

accesso aperto

Descrizione: Articolo principale
Tipologia: Publisher's version/PDF
Dimensione 503.21 kB
Formato Adobe PDF
503.21 kB Adobe PDF Visualizza/Apri
Pubblicazioni consigliate

Caricamento pubblicazioni consigliate

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2434/898372
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 3
  • ???jsp.display-item.citation.isi??? 5
social impact