An Elastic Model for Volcanology

✍ Scribed by Andrea Aspri

• Publisher: Springer International Publishing;Birkhäuser
• Year: 2019
• Tongue: English
• Leaves: 136
• Series: Lecture Notes in Geosystems Mathematics and Computing
• Edition: 1st ed. 2019
• Category: Library

✦ Synopsis

This monograph presents a rigorous mathematical framework for a linear elastic model arising from volcanology that explains deformation effects generated by inflating or deflating magma chambers in the Earth’s interior. From a mathematical perspective, these modeling assumptions manifest as a boundary value problem that has long been known by researchers in volcanology, but has not, until now, been given a thorough mathematical treatment. This mathematical study gives an explicit formula for the solution of the boundary value problem which generalizes the few well-known, explicit solutions found in geophysics literature. Using two distinct analytical approaches—one involving weighted Sobolev spaces, and the other using single and double layer potentials—the well-posedness of the elastic model is proven. An Elastic Model for Volcanology will be of particular interest to mathematicians researching inverse problems, as well as geophysicists studying volcanology.

✦ Table of Contents

Front Matter ....Pages i-x
From the Physical to the Mathematical Model (Andrea Aspri)....Pages 1-10
A Scalar Model in the Half-Space (Andrea Aspri)....Pages 11-51
Analysis of the Elastic Model (Andrea Aspri)....Pages 53-118
Back Matter ....Pages 119-126

✦ Subjects

Mathematics; Partial Differential Equations; Geophysics/Geodesy; Potential Theory; Mathematical Modeling and Industrial Mathematics