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Analysis Seminar

Thursday, October 12, 2017 - 3:00pm

Donghyun Lee

University of Wisconsin–Madison


University of Pennsylvania


When dilute charged particles are confined in a bounded domain, boundary effects are crucial for dynamics of particles which can be modeled by the Vlasov-Poisson-Boltzmann system. Considering a diffuse boundary condition, we construct a unique global-in-time solution in convex domains. This construction is based on L^2-L^\infty framework with a new weighted W^{1,p}-estimate of distribution functions and C^{2,\alpha}-estimate of self-consistent electric potentials. Furthermore we prove an exponential convergence of distribution functions toward a global Maxwellian.