Stability of Classical Shock Fronts for Compressible Hyperelastic Materials of Hadamard Type

This paper studies the uniform and weak Lopatinski\u{\i} conditions associated to classical (Lax) shock fronts of arbitrary amplitude for compressible hyperelastic materials Hadamard type in several space dimensions. Thanks seminal works Majda (Mem. Amer. Math. Soc. 43 (1983), no. 281; Mem. 41 275) M\'etivier (Trans. 296 (1986), pp. 431-479; Comm. Partial Diff. Eqs. 15 (1990), 7, 983-1028), condition ensures local-in-time, multidimensional, nonlinear stability such fronts. The function (also called determinant) shocks this large class is computed explicitly. information used establish terms parameters elastic moduli material.