We present the existence and uniqueness of strong solutions for the continuous coagulation-fragmentation equation with singular fragmentation and essentially bounded coagulation kernel using semigroup theory of operators. Initially, we reformulate the coupled coagulation-fragmentation problem into the semilinear abstract Cauchy problem (ACP) and consider it as the nonlinear perturbation of the linear fragmentation operator. The existence of the substochastic semigroup is proved for the pure fragmentation equation. Using the substochastic semigroup and some related results for the pure fragmentation equation, we prove the existence of global nonnegative, strong solution for the coagulation-fragmentation equation.
Coagulation, fragmentation, abstract Cauchy problem, semigroups of operators, existence & uniqueness
DAS, ARIJIT; DAS, NILIMA; and SAHA, JITRAJ
"An application of semigroup theory to the coagulation-fragmentation models,"
Turkish Journal of Mathematics: Vol. 45:
5, Article 28.
Available at: https://journals.tubitak.gov.tr/math/vol45/iss5/28