论文标题
在良好的边界条件下，线性非均匀矩方程的半空间
On Well-posed Boundary Conditions for the Linear Non-homogeneous Moment Equations in Half-space
论文作者
论文摘要
我们为半空间的线性非均匀毕业矩方程的适当性提出了必要且充分的条件。毕业生力矩系统基于HERMITE的扩展，并被视为Boltzmann方程的有效还原模型。在实心壁上，矩方程通常配备了麦克斯韦型边界条件，称为毕业边界条件。我们指出，对于非同质性半空间问题，毕业边界条件是不稳定的。得益于提出的标准，我们验证了一类改良边界条件的适当性。确保存在和唯一性的技术主要包括针对系数矩阵的精心设计的同时转换，以及与特征边界有关线性边界价值问题问题的Kreiss程序。稳定性是通过加权估计来确定的。同时，我们获得了解决方案的分析表达式，这可能有助于有效地解决半空间问题。
We propose a necessary and sufficient condition for the well-posedness of the linear non-homogeneous Grad moment equations in half-space. The Grad moment system is based on Hermite expansion and regarded as an efficient reduction model of the Boltzmann equation. At a solid wall, the moment equations are commonly equipped with a Maxwell-type boundary condition named the Grad boundary condition. We point out that the Grad boundary condition is unstable for the non-homogeneous half-space problem. Thanks to the proposed criteria, we verify the well-posedness of a class of modified boundary conditions. The technique to make sure the existence and uniqueness mainly includes a well-designed preliminary simultaneous transformation of the coefficient matrices and Kreiss' procedure about the linear boundary value problem with characteristic boundaries. The stability is established by a weighted estimate. At the same time, we obtain the analytical expressions of the solution, which may help solve the half-space problem efficiently.
