Search

We consider a nonlinear, hyperbolic population balance equation that incorporates both aggregation and collisional breakage events simultaneously. Our approach revolves around the development of a novel time-explicit finite volume scheme. Under a suitable time-step stability condition, we prove the convergence of the approximate solution for any non-uniform mesh. A first-order convergence is obtained by a thorough error analysis of the proposed scheme for a suitable choice of kernels. Finally, we compute some numerical test examples to explore the behavior of the solution in steady-state conditions as well as the occurrence of gelation phenomena. [ABSTRACT FROM AUTHOR]

In this article, the existence and uniqueness of global solutions to the discrete Safronov–Dubovskiǐ aggregation equation is studied. The unbounded aggregation kernel exhibits at most linear growth at infinity. The solution exhibits mass conservation property without any further restriction over the kernels. [ABSTRACT FROM AUTHOR]

In this paper, we prove the global existence and uniqueness of the solutions to the initial-value problem for the coagulation-fragmentation equation with singular coagulation kernel and multiple fragmentation kernel. The solution obtained in this case also satisfies the mass conservation law. The proof is based on strong convergence methods applied to suitably chosen unbounded coagulation kernels having singularities in both the coordinate axes and satisfying certain growth conditions, which can possibly reach up to a quadratic growth at infinity, and the fragmentation kernel covers a very large class of unbounded functions. [ABSTRACT FROM AUTHOR]