On the spatially inhomogeneous particle coagulation-condensation model
with singularity
Abstract
The spatially inhomogeneous coagulation-condensation process is an
interesting topic of study as the phenomenon’s mathematical aspects
mostly undiscovered and has multitudinous empirical applications. In
this present exposition, we exhibit the existence of a continuous
solution for the corresponding model with the following
\emph{singular} type coagulation kernel:
\[K(x,y)~\le~\frac{\left(
x +
y\right)^\theta}{\left(xy\right)^\mu},
~~\text{for}
~x, y \in (0,\infty),
\text{where}~ \mu
\in
\left[0,\tfrac{1}{2}\right]
\text{ and } ~\theta
\in [0, 1].\] The above-mentioned
form of the coagulation kernel includes several practical-oriented
kernels. Finally, uniqueness of the solution is also investigated.