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| The talk will present nonlinear evolution equations of fourth and sixth order in spatial derivatives, which arise in the quantum modeling of semiconductor and plasma physics, and describe the evolution of densities of charged particles in a quantum fluid. We report on some basic results known about equations: local in time existence of positive classical, global in time existence and the long time behaviour of weak nonnegative solutions, as well as on respective techniques used in the analysis. Interesting structural properties, like dissipation of the physical entropy and formal gradient flow structure with respect to the Wasserstein distance will be also discussed. |
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