Existence of a Solution to the Cauchy Problem for the Aggregation Equation in Hyperbolic Space

In hyperbolic space, we consider the Cauchy problem for the aggregation equation. Non-negative initial function is bounded and summable. We prove the existence of a weak solution on a small time interval. In the case where the kernel of the integral operator is smooth and rapidly decreases at infinity, the existence of a bounded solution on an arbitrary time interval is proved.