Local Well-Posedness of Vlasov–Poisson–Boltzmann Equation with Generalized Diffuse Boundary Condition

The Vlasov–Poisson–Boltzmann equation is a classical equation governing the dynamics of charged particles with the electric force being self-imposed. We consider the system in a convex domain with the Cercignani–Lampis boundary condition. We construct a uniqueness local-in-time solution based on an $$L^\infty $$-estimate and $$W^{1,p}$$-estimate. In particular, we develop a new iteration scheme along the characteristic with the Cercignani–Lampis boundary for the $$L^\infty $$-estimate, and an intrinsic decomposition of boundary integral for $$W^{1,p}$$-estimate.