A note on asymptotics of linear dissipative kinetic equations in bounded domains

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.

References in corpus (4)

• Geometric Correction for Diffusive Expansion of Steady Neutron Transport Equation
• Variational methods for the kinetic Fokker-Planck equation
• On a spatially inhomogeneous nonlinear Fokker-Planck equation: Cauchy problem and diffusion asymptotics
• Spectral gap formation to kinetic equations with soft potentials in bounded domain