The research project is about the propagation along the solution of evolution equations, as ODEs, parabolic or
hyperbolic PDEs or DDEs, of uncertainties in the initial value and in the parameters. The sizes of such uncertainties
are measured by relative errors. In particular, the interest is on the long-time behavior. The study considers both
exact solutions and numerical solutions and this latter case also the propagation along the solution of errors due to
the use of the numerical method is taking into account. In other terms, the project is concerned with the
determination and the study of “condition numbers” for evolution equations. These numbers quantify, in terms of
relative errors, how a perturbation in the data of a problem are magnified in the solution of this problem. Both
deterministic worst case perturbation and probabilistic average case perturbation will be considered.