The Continuous Coagulation Equation with Multiple Fragmentation
نویسندگان
چکیده
We present a proof of the existence of solutions to the continuous coagulation equation with multiple fragmentation whenever the kernels satisfy certain growth conditions. The proof relies on weak L compactness methods applied to suitably chosen approximating equations. The question of uniqueness is also considered.
منابع مشابه
Weak solutions to the continuous coagulation equation with multiple fragmentation
The existence of weak solutions to the continuous coagulation equation with multiple fragmentation is shown for a class of unbounded coagulation and fragmentation kernels, the fragmentation kernel having possibly a singularity at the origin. This result extends previous ones where either boundedness of the coagulation kernel or no singularity at the origin for the fragmentation kernel was assumed.
متن کاملGlobal strict solutions to continuous coagulation-fragmentation equations with strong fragmentation
In this paper we give an elementary proof of the unique, global-in-time solvability of the coagulation-(multiple) fragmentation equation with polynomially bounded fragmentation and particle production rates and a bounded coagulation rate. The proof relies on a new result concerning domain invariance for the fragmentation semigroup which is based on a simple monotonicity argument.
متن کاملStrongly Differentiable Solutions of the Discrete Coagulation-Fragmentation Equation
We examine an infinite system of ordinary differential equations that models the coagulation and fragmentation of clusters. In contrast to previous investigations, we allow multiple fragmentation to occur and our analysis does not involve finite-dimensional truncations of the system. Instead, we treat the problem as an infinite-dimensional differential equation, posed in an appropriate Banach s...
متن کاملGelation and Mass Conservation in Coagulation-fragmentation Models
The occurrence of gelation and the existence of mass-conserving solutions to the continuous coagulation-fragmentation equation are investigated under various assumptions on the coagulation and fragmentation rates, thereby completing the already known results. A non-uniqueness result is also established and a connection to the modified coagulation model of Flory is also made.
متن کاملThe Coagulation - Fragmentation Equation and Its Stochastic Counterpart
We consider a coagulation multiple-fragmentation equation, which describes the concentration ct(x) of particles of mass x ∈ (0,∞) at the instant t ≥ 0 in a model where fragmentation and coalescence phenomena occur. We study the existence and uniqueness of measured-valued solutions to this equation for homogeneous-like kernels of homogeneity parameter λ ∈ (0, 1] and bounded fragmentation kernels...
متن کامل