Identification of processes governing damage evolution in linear-elastic continua

In the beginning of this work we present a regularity result for second-order evolution equation which is essential for the mathematical analysis of inverse problems stemming from hyperbolic PDEs as well as for the implementation of respective regularization methods.
The remainder of this text then focuses on the identification of Nemytskii operators in nonlinear systems of differential equations.
To this end, we rigorously investigate a Kachanov-type damage evolution in a quasi-static elasticity setting for the possibility to retrieve the damage process from full-field measurements.
The novelty in this approach lies within the reconstruction of the operator modeling the right-hand side of the damage evolution equation that intimately couples damage and displacements.
We were able to come by all the ingredients necessary to implement iterative reconstruction methods.
We end the analytical part with proving the nonlinear tangential cone condition which is a necessary condition for many iterative solvers.
Numerical simulations and analysis conclude this work.