J. Banasiak, W. Lamb and M. Langer,
Strong fragmentation and coagulation with power-law rates,
J. Engrg. Math. 82 (2013), 199–215
Abstract:
Existence of global classical solutions to fragmentation and coagulation equations
with unbounded coagulation rates has been recently proved for initial conditions
with finite higher-order moments.
These results cannot be directly generalized to the most natural space of solutions
with finite mass and number of particles due to the lack of precise characterization
of the domain of the generator of the fragmentation semigroup.
In this paper we show that such a generalization is possible in the case
when fragmentation is described by power-law rates, which are commonly
used in engineering practice. This is achieved through direct estimates of the
resolvent of the fragmentation operator, which in this case is explicitly known,
proving that it is sectorial and carefully intertwining the corresponding
intermediate spaces with appropriate weighted L1 spaces.