We consider the asymptotic nonlinear stability of viscous shock profiles for an initial-boundary value problem of the scalar conservation laws with an artificial heat flux satisfying Cattaneo's law in the negative half line Double-struck capital R-=(-infinity,0)$$ {\mathrm{\mathbb{R}}}_{-} equal to \left(-\infty, 0\right) $$ with Dirichlet boundary condition. When the nonlinear flux function is assumed to be strictly convex and the unique global entropy solution of the corresponding Riemann problem of the resulting scalar conservation laws consists of shock wave with negative speed, it is show...
