Umeå universitets logga

We study the dynamic relaxation to equilibrium of the 1D dissipative Boltzmann equation with Maxwell interactions in classical H^s Sobolev spaces. In addition, we present a shrinkage analysis and decay estimates for the linearised 1D dissipative Boltzmann operator with such interactions. Based on this study, we explore the convergence in H^s and L¹ spaces for the linear and nonlinear models. This study extends classical results found in the literature given for spaces with weak topologies.