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Nonlinear Analysis: Theory, Methods & Applications, 2004The hyperbolic system \(u_t +f(u)_x =0\) is considered in the domain \(t>0\), \(x>\Psi (t)\). Assumptions on the flux \(f: \mathbb R^n \to \mathbb R^n\) are imposed to state that the system is of the Temple type. The boundary condition \(u(t,\Psi (t))=\) \(\widetilde{u}(t)\) is satisfied in the Dubois-LeFloch sense [\textit{F.
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