WG3 - Networks and similar structures
The cell cycle, as well as the exploitation of a biological resource or demographic models, lead to renewal equations (i.e., balance laws with possibly nonlocal boundary conditions) on graphs. Their analytic treatment has some features that resemble that of models for vehicular traffic on road networks. Coupled systems of PDEs of different types can then be stated on various geometric structures, in particular graphs or networks. While the development of a very general abstract theory comprising all these situations might look ineffective in this particular case, the use of subtle analytic tools in specific applications is likely to be highly productive.
- Apply the theory developed in WG1 and WG2 to DSNs.
- Develop the appropriate approach to study dynamical processes on multi-structures, especially hypergraphs and ramified spaces.
- Use the semigroup approach to study nonlinear dynamical systems on networks.
- In collaboration with WG5 test ad hoc numerical algorithms dedicated to specific models.