On an extension of the d’Alembert solution to initial–boundary value problems in multi-layered, multi-material domains

• The d’Alembert solution is extended to IBVPs in multi-layered, multi-material domains.
• The solution is exact and can be expressed in closed form.
• The solution is valid for continuous or generalized data.
• The solution method is based on the characteristic and a recurrence formula.

This work introduces a method for the exact solution of initial–boundary value problems for linear, one-dimensional conservation laws in multi-layered, multi-material domains. The method is based on the geometry of the solutions of such conservation laws and represents an extension of the d’Alembert solution to initial–boundary value problems in multi-layered, multi-material domains.