L. Kerr, W. Lamb and M. Langer,
Discrete fragmentation equations with time-dependent coefficients,
Discrete Contin. Dyn. Syst. Ser. S, to appear
Abstract:
We examine an infinite, linear system of ordinary differential equations
that models the evolution of fragmenting clusters, where each cluster is assumed
to be composed of identical units. In contrast to previous investigations into
such discrete-size fragmentation models, we allow the fragmentation coefficients
to vary with time.
By formulating the initial-value problem for the system as a non-autonomous
abstract Cauchy problem, posed in an appropriately weighted ℓ1 space,
and then applying results from the theory of evolution families,
we prove the existence and uniqueness of physically relevant, classical solutions
for suitably constrained coefficients.