Uniqueness of Transonic Shock Solutions to Euler-Poisson System with Varying Background Charges (Communications in Mathematical Research, 2024)
In this paper, we investigate a one-dimensional Euler-Poisson system with varying background charges, which are two different constants whenthe flow speed is less than and greater than the sound speed. Using the shockmatching method, we derive the properties of the solution trajectories and establish a monotonic relationship between the density at the nozzle exit and theshock position. This relationship demonstrates the existence and uniquenessof a transonic shock solution under suitable boundary conditions.