English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Open

We consider the dynamics of particle systems where the particles are confinedby impenetrable barriers to a bounded, possibly non-convex domain $\Omega$.When particles hit the boundary, we consider an instant change in velocity,which turns the systems describing the particle dynamics into an ODE withdiscontinuous right-hand side. Other than the typical approach to analyse sucha system by using weak solutions to ODEs with multi-valued right-hand sides(i.e., applying the theory introduced by Filippov in 1988), we establish theexistence of mild solutions instead. This solution concept is easier to workwith than weak solutions; e.g., proving uniqueness of mild solutions isstraight-forward, and mild solutions provide a solid structure for provingmany-particle limits.  We supplement our theory of mild solutions with an application to gradientflows of interacting particle energies with a singular interaction potential,and illustrate its features by means of numerical simulations on variouschoices for the (non-convex) domain $\Omega$.

Particle dynamics subject to impenetrable boundaries: existence and uniqueness of mild solutions