Thermal Science 2015 Volume 19, Issue suppl. 1, Pages: 13-23
https://doi.org/10.2298/TSCI15S1S13D
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Extension of fragmentation process in a kinetic-diffusive-wave system
Doungmo-Goufo Emile Franc (University of South Africa, Department of Mathematical Sciences, Florida, South Africa)
Atangana Abdon (University of the Free State, Faculty of Natural and Agricultural Sciences, Institute for Groundwater Studies, Bloemfontein, South Africa)
Alternative methods are used to set conditions and investigate, in the space
L1(R3 × R+ mdmdx) the well-posedness of a fractional fragmentation process in
a kinetic-diffusive-wave medium. In the analysis, three separate models of
diffusion are studied. Techniques like separation of variables and
subordination principle are used to finally prove that the Cauchy problem for
fractional fragmentation dynamics in a kinetic-diffusive-wave system is
well-posed and admits a solution operator that is positive and contractive.
This work brings a contribution that may lead to the full explanation of
strange phenomena like shattering and sudden appearance of an infinite number
of particles in a system that occur in the dynamics of fragmentation process
and which remain partially unsolved.
Keywords: fragmentation, kinetic-diffusive-wave process, fractional Cauchy problem, well-posedness, solution operators