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Strong fragmentation and coagulation with power-law rates. (English) Zbl 1360.35279

Summary: 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 \(L_1\) spaces.

MSC:

35Q82 PDEs in connection with statistical mechanics
35F25 Initial value problems for nonlinear first-order PDEs
35R09 Integro-partial differential equations
35A01 Existence problems for PDEs: global existence, local existence, non-existence
35A02 Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness
35Q92 PDEs in connection with biology, chemistry and other natural sciences
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