Goldstein-Taylor模型中最快衰变的跳跃率
Finding the jump rate for fastest decay in the Goldstein-Taylor model
摘要：
对于次强制线性动力学方程，我们首先制定一个优化问题的空间依赖的跳跃率，以找到最快的扰动衰减率。在Goldstein-Taylor模型中，我们证明了（i）对于局部最优跳跃率，谱隙由多个可能的退化特征向量确定;（ii）全局最快的衰减是以空间均匀的跳跃率获得的。我们的证明依赖于阻尼波方程的连接和薛定谔算子的谱理论的关系。
英文摘要：
For hypocoercive linear kinetic equations we first formulate an optimisation problem on a spatially dependent jump rate in order to find the fastest decay rate of perturbations. In the Goldstein-Taylor model we show (i) that for a locally optimal jump rate the spectral gap is determined by multiple, possible degenerate, eigenvectors and (ii) that globally the fastest decay is obtained with a spatially homogeneous jump rate. Our proofs rely on a connection to damped wave equations and a relationship to the spectral theory of Schr{ö}dinger operators.
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