Explicit solutions for a system of First-order partial differential equations

Abstract

In this paper we construct explicit weak solutions of a system of two partial differential equations in the quarter plane {(x, t) : x > 0, t > 0} with initial conditions at t = 0 and a weak form of Dirichlet boundary conditions at x = 0. This system was first studied by LeFloch [9], where he constructed explicit formula for the weak solution of pure initial value problem.