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Demonstrates exponential decay to equilibrium in semiconductor devices, indicating new insights on non-linear kinetics.
A kinetic model for semiconductor devices is considered on a flat torus. We prove exponential decay to equilibrium for this non-linear kinetic model by hypocoercivity estimates. This seems to be the first hypocoercivity result for this nonlinear kinetic equation for semiconductor devices without smallness assumptions. The analysis benefits from uniform bounds of the solution in terms of the equilibrium velocity distribution.
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Pirner et al. (2026) studied this question.
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