Special Session 99: Emerging Trends in Analysis and Control of PDEs

Inverse problems for Kelvin--Voigt viscoelastic and Moore--Gibson--Thompson equations
Jone Apraiz
University of the Basque Country
Spain
Co-Author(s):    Rodrigo Lecaros (Federico Santa Mar\`{i}a Technical University, Chile) and Sebasti\`{a}n Zamorano (University of Deusto, Spain).
Abstract:
In this talk we will consider inverse coefficient problems for two evolution models with relaxation structure: a Kelvin--Voigt viscoelastic system and the Moore--Gibson--Thompson equation arising in nonlinear acoustics. In both cases, we will establish Lipschitz stability estimates for the recovery of a space-dependent damping coefficient from a single measurement. This research extends Carleman-based inverse theory to third-order-in-time acoustic models and provides a unified framework for inverse problems in relaxation-type evolution equations. This is a joint research project in collaboration with Rodrigo Lecaros (Federico Santa Mar\`{i}a Technical University, Chile) and Sebasti\`{a}n Zamorano (University of Deusto, Spain).