Acta mathematica scientia,Series A ›› 2021, Vol. 41 ›› Issue (6): 1853-1863.

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Optimal Exponential Decay for the Linear Inhomogeneous Boltzmann Equation with Hard Potentials

Baoyan Sun*()   

  1. School of Mathematics and Information Sciences, Yantai University, Shandong Yantai 264005
  • Received:2021-07-22 Online:2021-12-26 Published:2021-12-02
  • Contact: Baoyan Sun
  • Supported by:
    the Scientific Research Foundation of Yantai University(2219008)


In this paper, we consider the asymptotic behavior of solutions to the linear spatially inhomogeneous Boltzmann equation for hard potentials in the torus. We obtain an optimal rate of exponential convergence towards equilibrium in a Lebesgue space with polynomial weight $L_{v}^{1} L_{x}^{2}\left(\langle v\rangle^{k}\right)$. This model is analyzed from a spectral point of view and from the point of view of semigroups. Our strategy is taking advantage of the spectral gap estimate in the Hilbert space with inverse Gaussian weight, the factorization argument and the enlargement method.

Key words: Linear Boltzmann equation, Hard potentials, Polynomial weight, Spectral gap, Exponential decay

CLC Number: 

  • O175