标题： 谱分解和衰减到大致确定的解对于一个简化的BGK模型 显示英文标题

标题： Spectral decomposition and decay to grossly determined solutions for a simplified BGK model

摘要： 在Carty工作的基础上，我们证明了简化的一维BGK模型的$H^1$解在$L^2$中指数衰减到Truesdell和Muncaster定义的全局确定解的一个子类。 在此过程中，我们确定了相关非自伴线性化算子的谱和广义本征函数，并推导了相关的广义傅里叶变换和帕塞瓦尔恒等式。 值得注意的是，我们的分析使用了起源于量子力学的刚化空间技术，这些技术由Ljance等人适应于非自伴情况。 显示英文摘要

摘要： Extending work of Carty, we show that $H^1$ solutions of a simplified 1D BGK model decay exponentially in $L^2$ to a subclass of the class of grossly determined solutions as defined by Truesdell and Muncaster. In the process, we determine the spectrum and generalized eigenfunctions of the associated non-selfadjoint linearized operator and derive the associated generalized Fourier transform and Parseval's identity. Notably, our analysis makes use of rigged space techniques originating from quantum mechanics, as adapted by Ljance and others to the nonselfadjoint case.