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 Tools annual

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 Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

We prove the following asymptotic behavior for solutions to the generalizedBecker-D\"oring system for general initial data: under a detailed balanceassumption and in situations where density is conserved in time, there is acritical density $\rho_s$ such that solutions with an initial density $\rho_0\leq \rho_s$ converge strongly to the equilibrium with density $\rho_0$, andsolutions with initial density $\rho_0 > \rho_s$ converge (in a weak sense) tothe equilibrium with density $\rho_s$. This extends the previous knowledge thatthis behavior happens under more restrictive conditions on the initial data.The main tool is a new estimate on the tail of solutions with density below thecritical density

Asymptotic behaviour of solutions to the generalized Becker–Döring equations for general initial data