论文标题
有限差异方案的Leray-Gårding方法。 ii。平滑的越过模式
The Leray-Gårding method for finite difference schemes. II. Smooth crossing modes
论文作者
论文摘要
在[COU15]一种乘数技术中，回到leray和gårding以获得标量双曲偏微分方程，已扩展到用于进化问题的有限差异方案的背景。 [COU15]中分析的关键点是，当将初始差异操作员乘以合适的数量时，要获得离散的能量散失平衡法。在[COU15]中实现了所有模式分离的，在[COU15]中实现了能量和耗散功能。我们在这里放松这个假设，并以与[COU15]相同的乘数构建，当某些模式交叉时，能量和耗散功能。通过遵循[COU15]的参数，在更广泛的上下文中推导了完全离散的Hy-perbolic初始边界价值问题的半群估计。
In [Cou15] a multiplier technique, going back to Leray and Gårding for scalar hyperbolic partial differential equations, has been extended to the context of finite difference schemes for evolutionary problems. The key point of the analysis in [Cou15] was to obtain a discrete energy-dissipation balance law when the initial difference operator is multiplied by a suitable quantity. The construction of the energy and dissipation functionals was achieved in [Cou15] under the assumption that all modes were separated. We relax this assumption here and construct, for the same multiplier as in [Cou15], the energy and dissipation functionals when some modes cross. Semigroup estimates for fully discrete hy-perbolic initial boundary value problems are deduced in this broader context by following the arguments of [Cou15].
