The Global Solutions of the Scalar Nonconvex Conservation Law with Boundary Condition (Journal of Partial Differential Equations, 2020)
Using the polygonal approximations method, we construct the global approximate solution of the initial boundary value problem (1.1)-(1.3) for the scalar nonconvex conservation law, and prove its convergence. The crux of this work is to clarify the behavior of the approximations on the boundary x = 0.
Keywords: Scalar conservation law; nonconvex; boundary condition; polygonal approximations method