Growth–fragmentation–coagulation equations with unbounded coagulation kernels

A Direct Simulation Method for the Coagulation-Fragmentation. Equations with Multiplicative Coagulation Kernels

This paper introduces a fast method of direct simulation for the stochastic process corresponding to coagulation-fragmentation dynamics with multiplica-tive coagulation kernels. Convergence results and error estimates are proved in a case where the corresponding deterministic equations are known to have a unique solution, as well as a relative compactness property of the family of stochastic pr...

COLLOCATION METHOD FOR FREDHOLM-VOLTERRA INTEGRAL EQUATIONS WITH WEAKLY KERNELS

In this paper it is shown that the use of‎ ‎uniform meshes leads to optimal convergence rates provided that‎ ‎the analytical solutions of a particular class of‎ ‎Fredholm-Volterra integral equations (FVIEs) are smooth‎.

Coagulation Equations with Gelation

Smoluchowski's equation for rapid coagulation is used to describe the kinetics of gelation, in which the coagulation kernel Kij models the bonding mechanism. For different classes of kernels we derive criteria for the occurrence of gelation, and obtain critical exponents in the preand postgelation stage in terms of the model parameters; we calculate bounds on the time of gelation to, and give a...

Integral Equations with Contrasting Kernels

0 C(t, s)x(s)ds with sharply contrasting kernels typified by C∗(t, s) = ln(e + (t − s)) and D∗(t, s) = [1 + (t − s)]. The kernel assigns a weight to x(s) and these kernels have exactly opposite effects of weighting. Each type is well represented in the literature. Our first project is to show that for a ∈ L[0,∞), then solutions are largely indistinguishable regardless of which kernel is used. T...

Szegö Kernels for Certain Unbounded Domains