Kinetic Description of Multiscale Phenomena
The Annual Kinetic FRG Meeting
September 21-25, 2009
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Coagulation transport with diffusion
Dr. Pavel Dubovsky
Stevens Institute of Technology
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Abstract: The coagulation--fragmentation kinetics describes the evolution of particles under the influence of convection and diffusion and serves as an important example of an infinite-dimensional convection-diffusion dynamic system. The nonlinear collision operator in its domain satisfies the mass conservation law. To prove the existence theorem for both the transport equation and the equation with diffusion we use a version of the maximum principle and establish the global in time existence, uniqueness, and stability theorems of classical solutions in an important subclass of bounded kinetic coefficients. Besides the conservation law and the maximum principle, the results are based on a new uniform priori estimate for the "tails" of the series involved in the definition of the collision operator. Also, we show the uniqueness and the stability with respect to the small perturbations of both initial data and kinetic coefficients. The new estimates allow to prove the vanishing diffusion limit when the scaling parameter goes to zero. If time allows, we generalize the regularity results towards other infinite-dimensional convection-diffusion systems.
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