2021/04/14 by Bertrand Lods, Lods, Bertrand, Mustapha Mokhtar‐Kharroubi +1
Computer Science · Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Gas Dynamics and Kinetic Theory #Mathematical Biology Tumor Growth #Optimization and Variational Analysis
paper · doi:10.48550/arxiv.2104.06674
openalex publication_date 2021/04/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper provides a new tauberian approach to the study of quantitative time asymptotics of collisionless transport semigroups with general diffuse boundary operators. We obtain an (almost) optimal algebraic rate of convergence to equilibrium under very general assumptions on the initial datum and the boundary operator. The rate is prescribed by the maximal gain of integrability that the boundary operator is able to induce. The proof relies on a representation of the collisionless transport semigroups by a (kind of) Dyson-Phillips series and on a fine analysis of the trace on the imaginary axis of Laplace transform of remainders (of large order) of this series. Our construction is systematic and is based on various preliminary results of independent interest.