Global solvability of the Cauchy problem for a system of equations in the nonlinear theory of elasticity
The author considers the Cauchy problem for an isentropic system in the nolinear theory of elasticity in Eulerian coordinates. The goal is to prove a global existence theorem for the functional solution to this problem. The proof of the theorem is based on the viscosity method; however, the present case is special in some important respects. First, the subset of equations for distortion has a nonconservative form. Second, the functional solution can be reduced to a function belonging to the Lebesgue space.
scientific article; zbMATH DE number 1427869