Robert Szalai (Bristol, UK)
Abstract:
Non-smooth dynamics comes from simplifying assumptions that harsh nonlinearities, such as friction, which can be described by vector fields with discontinuous right-hand side. Filippov’s definition of solution is used almost exclusively to investigate the general properties of non-smooth systems. Using this definition many intriguing features emerge, such as forward time non-uniqueness, the combinatorial proliferation of bifurcations and the apparent lack of complete bifurcation theory for higher (>2) dimensions. The question is whether we can do better, after all classical physics as we know it should be deterministic. The answer is a strong yes, which can be achieved by taking into account wave propagation in media, in elastic bodies, electromagnetic field, etc. The extra physics reveals a simple extension to Filippov’s definition that takes into account the fast dynamics of travelling waves coupled with slowly varying system variables. The result is a non-smooth system with unique solutions, which collapses to Filippov’s definition for infinite wave-speed
The seminars are organized by the Mathematics section at DTU Compute. The section is organizing a lecture series in Multi-Scale Dynamical Systems with 5 events until the end of the year.
All are welcome.
We thank DTU Compute’s Strategic Fond for financial support.