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Discrete coagulation--fragmentation systems in weighted $\ell^1$ spaces
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abstract
We study an infinite system of ordinary differential equations that models the evolution of coagulating and fragmenting clusters, which we assume to be composed of identical units. Under very mild assumptions on the coefficients we prove existence, uniqueness and positivity of solutions of a corresponding semi-linear Cauchy problem in a weighted $\ell^1$ space. This requires the application of novel results, which we prove for abstract semi-linear Cauchy problems in Banach lattices where the non-linear term is defined only on a dense subspace.
Forward citations
Cited by 2 Pith papers
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Fragmentation-coagulation processes with advection or diffusion in space
Spatially transported fragmentation-coagulation equations generate positive C0-semigroups in weighted L1 spaces and admit local classical solutions with unbounded coagulation under explicit rate conditions.
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Continuous fragmentation equations in weighted $L^1$ spaces
Continuous fragmentation equations with possibly non-mass-conserving kernels admit unique classical solutions in suitably weighted L1 spaces, and the associated semigroup is analytic for a large class of weights and kernels.
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