Applying Functional Analytic Techniques to Evolution Equations

Lamb, Wilson

doi:10.1007/978-3-319-11322-7_1

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“…To the best of our knowledge, the microscopic modeling of this kind of merging is performed here for the first time. All previous theories, see, e.g., [1,2,3,4,10,12,13], deal with the densities of the particles and hence do not take into account the corpuscular structure of the system. However, we do not take into account the particle mass, which is supposed to be done in an extension of the present model.…”

Section: Introductionmentioning

confidence: 99%

A kinetic equation for repulsive coalescing random jumps in continuum

Pilorz

2016

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A continuum individual-based model of hopping and coalescing particles is introduced and studied. Its microscopic dynamics are described by a hierarchy of evolution equations obtained in the paper. Then the passage from the micro-to mesoscopic dynamics is performed by means of a Vlasov-type scaling. The existence and uniqueness of the solutions of the corresponding kinetic equation are proved.2010 Mathematics Subject Classification. 60K35; 35Q83; 82C22.

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