Global Analysis of a Discrete Nonlocal and Nonautonomous Fragmentation Dynamics Occurring in a Moving Process
We use a double approximation technique to show existence result for a nonlocal and nonautonomous fragmentation dynamics occurring in a moving process. We consider the case where sizes of clusters are discrete and fragmentation rate is time, position, and size dependent. Our system involving transpo...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/484391 |
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| Summary: | We use a double approximation technique to show existence result for a nonlocal and nonautonomous
fragmentation dynamics occurring in a moving process. We consider the case where
sizes of clusters are discrete and fragmentation rate is time, position, and size dependent. Our
system involving transport and nonautonomous fragmentation processes, where in addition, new
particles are spatially randomly distributed according to some probabilistic law, is investigated by
means of forward propagators associated with evolution semigroup theory and perturbation theory.
The full generator is considered as a perturbation of the pure nonautonomous fragmentation
operator. We can therefore make use of the truncation technique (McLaughlin et al., 1997), the resolvent approximation
(Yosida, 1980), Duhamel formula (John, 1982), and Dyson-Phillips series (Phillips, 1953) to establish the existence of a solution
for a discrete nonlocal and nonautonomous fragmentation process in a moving medium, hereby,
bringing a contribution that may lead to the proof of uniqueness of strong solutions to this type of
transport and nonautonomous fragmentation problem which remains unsolved. |
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| ISSN: | 1085-3375 1687-0409 |