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

In this paper we study a class of coagulation equations including a sourceterm that injects in the system clusters of size of order one. The coagulationkernel is homogeneous, of homogeneity $\gamma < 1$, such that $K(x,y)$ isapproximately $x^{\gamma + \lambda} y^{-\lambda}$, when $x$ is larger than $y$.We restrict the analysis to the case $\gamma + 2 \lambda \geq 1 $. In thisrange of exponents, the transport of mass toward infinity is driven bycollisions between particles of different sizes. This is in contrast with thecase when $\gamma + 2 \lambda <1$. In that case, the transport of mass towardinfinity is due to the collision between particles of comparable sizes. In thecase $\gamma+2\lambda\geq 1$, the interaction between particles of differentsizes leads to an additional transport term in the coagulation equation thatapproximates the solution of the original coagulation equation with injectionfor large times. We prove the existence of a class of self-similar solutionsfor suitable choices of $\gamma $ and $\lambda$ for this class of coagulationequations with transport. We prove that for the complementary case suchself-similar solutions do not exist.

Long-time asymptotics for coagulation equations with injection that do not have stationary solutions