论文标题
光谱分解和腐烂至简化BGK模型的严格确定的溶液
Spectral decomposition and decay to grossly determined solutions for a simplified BGK model
论文作者
论文摘要
为了扩展Carty的工作，我们表明，简化的1D BGK型号的$ H^1 $解决方案以$ L^2 $的形式呈指数型衰减，向Truesdell和Muncaster定义的总确定解决方案的子类的子类。在此过程中，我们确定了相关的非频谱线性化运算符的频谱和广义特征，并得出了相关的广义傅立叶变换和parseval的身份。值得注意的是，我们的分析利用了源自量子力学的操纵空间技术，该技术由Ljance和其他人改编为非官方偶数。
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.
