Vlasov Poisson Boltzmann Equation in Bounded Domains
Explore the dynamics of dilute charged particles confined in bounded domains through this lecture on the Vlasov-Poisson-Boltzmann system. Delve into the crucial boundary effects and their impact on particle behavior. Learn about the construction of a unique global-in-time solution in convex domains, based on an L2-L∞ framework incorporating new weighted W1,p-estimates of distribution functions and C2,α-estimates of self-consistent electric potentials. Discover the proof of exponential convergence of distribution functions toward a global Maxwellian. Gain insights into advanced concepts in kinetic theory and mathematical physics during this 47-minute presentation from the Hausdorff Junior Trimester Program on Kinetic Theory at the Hausdorff Center for Mathematics.