论文标题
具有I型特征边界双曲线松弛系统的边界条件
Boundary Conditions for Hyperbolic Relaxation Systems with Characteristic Boundaries of Type I
论文作者
论文摘要
这项工作与具有特征边界的一维双曲松弛系统的边界条件有关。我们假设弛豫系统满足先前第二作者提出的结构稳定条件，并且边界是I型的特征（弛豫系统的特征，但对于相应的平衡系统而言，非特征性）。对于这种特征性的初始界价问题，我们提出了经过改进的广义Kreiss条件（GKC）。这将第二作者提出的非特征界限提出的GKC扩展到了当前的特征案例。在此修改后的GKC下，我们得出了减少的边界条件，并通过将能量估计与拉普拉斯变换相结合来验证其有效性。此外，我们展示了非线性问题的边界层的存在。
This work is concerned with boundary conditions for one-dimensional hyperbolic relaxation systems with characteristic boundaries. We assume that the relaxation system satisfies the structural stability condition proposed by the second author previously and the boundary is characteristic of type I (characteristic for the relaxation system but non-characteristic for the corresponding equilibrium system). For this kind of characteristic initial-boundary-value problems, we propose a modified Generalized Kreiss condition (GKC). This extends the GKC proposed by the second author for the non-characteristic boundaries to the present characteristic case. Under this modified GKC, we derive the reduced boundary condition and verify its validity by combining an energy estimate with the Laplace transform. Moreover, we show the existence of boundary-layers for nonlinear problems.
