The authors study the following continuous model of a coagulation: \[ \frac{\partial \phi}{\partial t}=\int_{0}^\infty a(\psi+\rho,\rho) \phi(\psi+\rho,t)\phi(\rho,t)d\rho -\int_{0}^\infty a(\psi,\rho) \phi(\psi,t)\phi(\rho,t)d\rho, \] with initial condition \[ \phi(\psi,0)=\phi^{in}(\psi)\geq 0, \] where \(\phi(\sigma, t)\) denotes the concentration of particles of volume \(\sigma\in [0,\infty)\) at time \(t \geq 0\). The non-negative quantity \(a(\psi,\rho)\) represents the coagulation rate at which particles of volume \(\psi\) and particles of volume \(\rho\) interact to produce particles of volume \(|\psi-\rho|\).
The main goal of the paper is to obtain sufficient conditions for existence and uniqueness of solutions for the above model.