Construction of Boundary Conditions for Hyperbolic Relaxation Approximations III: The Linearized Suliciu Model With Characteristic Boundaries

Abstract. This is our third work in the series on constructing boundary conditions for hyperbolic relaxation systems. Here, we focus on the linearized Suliciu model with characteristic boundaries. Assuming that appropriate initial and boundary conditions for the corresponding equilibrium system are given, we construct certain boundary conditions for the Suliciu model by means of a three-scale asymptotic expansion so that the resultant initial boundary value problems are asymptotically equivalent to the given problem. The constructed boundary conditions are demonstrated to be strictly dissipative. Moreover, we choose initial data compatible with the boundary conditions. Finally, we validate the constructed boundary conditions by showing the convergence of the solutions to the resultant initial boundary value problems, as the relaxation time tends to zero, toward the solution to the given problem.