Mathematical Mechanics and Inverse Problems

Researchers

Coordinators of Mathematical Mechanics area:  Carlos Conca and  Jorge San Martín
Coordinators of Inverse Problems area:   Jaime Ortega and Axel Osses

About the research group

The group has been developing research in uniqueness, stability, and reconstruction algorithms for inverse problems in PDEs, in the mathematical analysis and numerical methods for PDEs in fluid and solid mechanics, and in control and homogenization of PDEs. For the new period, the focus will be in analysis and modeling of inverse problems in wave propagation, fluids and heat transfer. This includes the study of inverse problems in fluid and solid mechanics and numerical reconstruction with partial data (Navier- Stokes, elasticity, viscoelasticity), inverse problems for hypoelliptic equations (degenerate parabolic, Kolmogorov, Grushin equations) and inverse problems for shape/topology (Muskat problem, free boundary problems, optimal distribution in transmission problems). At the same time, the group will continue developing new methods of direct and inverse modeling connected with emerging applied mathematical research relevant for Chilean development in astroinformatics (interferometry), in biomechanics (heart modeling, nuclear medicine, elastography, MRI) and in mining (source time reversal, rock and fracture dynamics, control and stabilization of waves).