EXISTENCE AND UNIQUENESS FOR SPATIALLY INHOMOGENEOUS COAGULATION CONDENSATION EQUATION WITH MULTIPLE FRAGMENTATION

Abstract

We study the spatially inhomogeneous coagulation condensation process with multiple fragmentations, proving the existence of a continuous solution of the model equation corresponding to the coagulation kernel

$$K(x,y)\le k_0+k_1(x^{\alpha }+y^{\alpha }) \text{for} x,y\in [0,\infty ), \text{where} \alpha \in \left[0,1\right],k_0,k_1\ge 0,$$

with at least one of $k_0$ and $k_1$ is nonzero. This form of the coagulation kernel includes several practical kernels. The study includes the fragmentation part in the model equation and considers multiple fragmentation kernels. Finally, the uniqueness of the solution is also investigated.