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/

Global: Zendy Plus annual

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

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We discuss the long-time behaviour of solutions to Smoluchowski's coagulationequation with kernels of homogeneity one, combining formal asymptotics,heuristic arguments based on linearization, and numerical simulations. The caseof what we call diagonally dominant kernels is particularly interesting. Hereone expects that the long-time behaviour is, after a suitable change ofvariables, the same as for the Burgers equation. However, for kernels that areclose to the diagonal one we obtain instability of both, constant solutions andtraveling waves and in general no convergence to N-waves for integrable data.On the other hand, for kernels not close to the diagonal one these structuresare stable, but the traveling waves have strong oscillations. This hasimplications on the approach towards an N-wave for integrable data, which isalso characterized by strong oscillations near the shock front.

Instabilities and oscillations in coagulation equations with kernels of homogeneity one