The workshop, organized under the sponsorship of the Istituto Nazionale di Alta Matematica, in collaboration with theIstituto delle Applicazioni del Calcolo of the Italian National Research Council, aims at bringing altogether skilled European researchers in both Mathematical Analysis andNumerical Computing fields, both belonging to various modern Applied Mathematics areas, in order to promote both interdisciplinarity and complementary expertise.

• on the one (analytical) hand, a markedly important question is raised by recent ill-posedness results for multi-dimensional (2D) hyperbolic systems of balance laws. It was previously conjectured by Elling that unclear numerical phenomena, like e.g. carbuncles in supersonic 2D simulations, were related to a lack of uniqueness for multi-D problems. Another (related) point is the study of hyperbolic systems posed on smooth manifolds, some of which, mostly multi-D, can be relevant for General Relativistic models.

• on the other (computational) hand, pseudo-inverse numerical methods were successfully applied to 1D fourth-order diffusion equations. Novel derivations of well-balanced schemes (along with 2D extensions) were proposed for linear kinetic equations, to compare with methods based on Case’s solutions methods.

Other areas of application may be considered, too: for instance mathematical biology, aggregate’s dynamics, and car/pedestrian traffic modeling.

Organizers: Laurent Gosse and Roberto Natalini