Datum predavanja: ponedjeljak, 7.7.2025.
Vrijeme predavanja: 15h

Juan Ricardo Muñoz Galeano, UNIDU
Title: Inverse Problems in the Wave Equation

Abstract:
Inverse problems for the wave equation seek to recover an unknown potential from boundary observations of the solution. The analysis relies on Hadamard’s framework of well-posedness, ensuring existence, uniqueness, and stability. A key tool is the Carleman estimate, a weighted inequality that enables quantitative unique continuation and stability results for hyperbolic operators. By constructing suitable weights, one establishes bounds linking variations in boundary fluxes to differences in the potential. These theoretical results underpin reconstruction algorithms based on convex regularization and variational principles. Recent developments extend this reconstruction framework through neural networks, where learning-based models approximate the inverse map.