  We take into account a coagulation model that simulates a distinct kind of
dynamics. In this model, two particles collide to produce a single particle,
but the resulting particle decreases in size, allowing each particle to be
fully identified by its size. It is demonstrated that the corresponding
evolving integral partial differential equation has solutions for product-type
coagulation kernels i.e. $0 \le \mathfrak{K}(\varrho, \varsigma)=
\mathfrak{K}(\varsigma, \varrho)=r(\varsigma) r(\varrho)+\alpha(\varsigma,
\varrho), (\varsigma, \varrho)\in \mathbb{R}_+^2$ and $\sup_{\varsigma \in
[0,R]} \frac{\mathfrak{K}(\varsigma, \varrho)}{\varrho} \to 0 \ \mbox{as} \
\varrho \to \infty$.
