Department of Mathematics - Seminar on Applied Mathematics - Unique and stable determination of the obstacle by finitely many far-field measurements

In this talk, I will discuss the uniqueness and stability aspects of identifying the obstacles using a finite number of far-field measurements. Uniqueness is primarily contingent upon the unique geometric structure exhibited by Laplacian eigenfunctions near corners. We achieve stable determination of convex polygonal impedance obstacles through a single far-field measurement. Our stability estimates establish explicit relationships between the geometric characteristics of the obstacle and the order of vanishing of the wave field at specific corner points.