On the initial boundary value problem for Temple systems
The 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. Dubois} and \textit{P. LeFloch}, J. Differ. Equations 71, No. 1, 93--122 (1988; Zbl 0649.35057)]. The initial and boundary-data functions are BV-functions. Global existence of a weak entropy solution is established. Stability of solutions is proved in the \(L^1\)-norm.
weak entropy solution is established. Stability in the \(L^1\)-norm
scientific article; zbMATH DE number 2101853