## Farooq Asma

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.