Abstract

We establish $L^2$-exponential decay properties for linear dissipative kinetic equations, including the time-relaxation and Fokker–Planck models, in bounded spatial domains with general boundary conditions that may not conserve mass. Their diffusion asymptotics in $L^2$ is also derived under general Maxwell boundary conditions. The proofs are simply based on energy estimates together with previous ideas from $L^2$-hypocoercivity and relative entropy methods.

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