论文标题
网络上的线性双曲系统
Linear Hyperbolic Systems on Networks
论文作者
论文摘要
我们研究一般（可能是非本地边界条件）下一维偏微分方程的双曲系统。可以在我们相当灵活的形式主义中重新重新构建大量的进化方程，无论是单个一维间隔还是在一般网络上，这可以重新构建，这概括了一阶减少的经典技术。我们研究前进和向后良好的态度；此外，我们在边界条件和一阶降低的系数以及相关环境空间的一阶降低中都提供了必要和充分的条件，以在控制系统的流动下是不变的。研究了几个例子。
We study hyperbolic systems of one-dimensional partial differential equations under general, possibly non-local boundary conditions. A large class of evolution equations, either on individual 1-dimensional intervals or on general networks, can be reformulated in our rather flexible formalism, which generalizes the classical technique of first-order reduction. We study forward and backward well-posedness; furthermore, we provide necessary and sufficient conditions on both the boundary conditions and the coefficients arising in the first-order reduction for a given subset of the relevant ambient space to be invariant under the flow that governs the system. Several examples are studied.
