In this study, the interaction of waves in the zero-pressure Euler equations with a Coulomb-like friction term is considered, which is equivalent to the Riemann problem with three constant initial states for the zero-pressure Euler equations. By solving generalized Rankine–Hugoniot relations under suitable entropy conditions, four different structures of explicit solutions are obtained uniquely, in which the interactions among contact discontinuity, vacuum, and delta shock are presented.

Aiming at the problem of low global convergence and local convergence rate of trust region interior points of bounded variable constrained nonlinear equations, a trust region interior point algorithm for bounded variable constrained nonlinear equations under edge calculation is designed. By constructing the basic function form of nonlinear equations constrained by bounded variables, the boundary of nonlinear equations is determined by Gauss Newton iterative process to ensure the global convergence of changes; solve the original objective function, analyze the trust region subproblem of the unconstrained optimization problem, and generate an acceptable region. The region is generated through two-dimensional example interpretation. The interior points in the acceptable region are determined by the primal dual interior point method, and the interior points in the acceptable region are optimized. With the help of edge calculation, the trust region interior point programming model of bounded variable constrained nonlinear equations is designed to realize the algorithm design. The experimental results show that the designed algorithm can improve the trust region interior point global convergence and local convergence rate of nonlinear equations with bounded variable constraints.