Special Session 48: Recent Advances in Nonlinear PDEs and Inverse Problems

Recovery of nonlinear material parameters in a quasilinear Lam\`e system
David Johansson
Aarhus University
Denmark
Co-Author(s):    Yavar Kian
Abstract:
I will discuss the identifiability of a nonlinear tensor in a quasilinear elliptic system, which is inspired by elasticity theory. As measurements we use point measurements at finitely many boundary points of the conormal derivative (or traction) of solutions generated by Dirichlet data (or boundary displacement) in the space of first order polynomials. By a linearization argument, we show that this data uniquely determines a nonlinear but space-independent tensor. Measurements in a single point is sufficient in the case of an isotropic tensor, while several points are used in the anisotropic case.