Global stability for an inverse problem in soil-structure interaction

TL;DR

This paper establishes a global stability estimate for an inverse problem involving the determination of the Winkler subgrade reaction coefficient in a soil-structure interaction model, based on interior deflection measurements.

Contribution

It provides the first global Hölder stability result for the inverse problem of identifying the subgrade reaction coefficient in a thin elastic plate model.

Findings

Proves a global Hölder stability estimate under mild regularity assumptions.

Demonstrates the uniqueness of the inverse problem solution.

Provides theoretical foundation for reliable soil-structure interaction analysis.

Abstract

We consider the inverse problem of determining the Winkler subgrade reaction coefficient of a slab foundation modelled as a thin elastic plate clamped at the boundary. The plate is loaded by a concentrated force and its transversal deflection is measured at the interior points. We prove a global H\"{o}lder stability estimate under (mild) regularity assumptions on the unknown coefficient.