Linear and NonLinear Stability for the Kinetic Plasma Sheath on a Bounded Interval

.Plasma sheaths are inhomogeneous stationary states that form when a plasma is in contact with an absorbing wall. We prove linear and nonlinear stability of a kinetic sheath stationary state for a Vlasov–Poisson-type system in a bounded interval. Notably, in the linear setting, we obtain exponential decay of the fluctuation, provided the rate of injection of particles at equilibrium is smaller than the rate of absorption at the wall. In the nonlinear setting, we prove a similar result for a small enough equilibrium and a small localized perturbation of the equilibrium.KeywordsVlasov–Poisson equationsboundary value problemplasma sheathlinear stabilitynonlinear stabilityfirst order delayed integral equationnon linear Poisson equationexit geometric conditionsMSC codes35Q8382B4082C40