While the quasilinear isothermal Euler equations are an excellent model for gas pipeline flow, the operation of the pipeline flow with high pressure and small Mach numbers allows us to obtain approximate solutions by a simpler semilinear model. We provide a derivation of the semilinear model that shows that the semilinear model is valid for sufficiently low Mach numbers and sufficiently high pressures. We prove an existence result for continuous solutions of the semilinear model that takes into account lower and upper bounds for the pressure and an upper bound for the magnitude of the Mach number of the gas flow. These state constraints are important both in the operation of gas pipelines and to guarantee that the solution remains in the set where the model is physically valid. We show the constrained exact boundary controllability of the system with the same pressure and Mach number constraints.

虽然拟线性等温欧拉方程是天然气管道流动的优秀模型，但高压和小马赫数管道流动的运行使我们能够通过更简单的半线性模型获得近似解。我们提供了半线性模型的推导，表明半线性模型对于足够低的马赫数和足够高的压力是有效的。我们证明了半线性模型的连续解的存在性结果，该模型考虑了压力的下限和上限以及气流马赫数大小的上限。这些状态约束对于输气管道的运行以及确保解保持在模型在物理上有效的集合中都很重要。