THERMAL SCIENCE

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Emile Franc Doungmo Goufo

,

Abdon Atangana

EXTENSION OF FRAGMENTATION PROCESS IN A KINETIC-DIFFUSIVE-WAVE SYSTEM

ABSTRACT
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
PAPER SUBMITTED: 2014-10-10
PAPER REVISED: 2015-03-15
PAPER ACCEPTED: 2015-03-18
PUBLISHED ONLINE: 2015-08-02
DOI REFERENCE: https://doi.org/10.2298/TSCI15S1S13D
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2015, VOLUME 19, ISSUE Supplement 1, PAGES [S13 - S23]
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Extension of fragmentation process in a kinetic-diffusive-wave system

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