Global existence of classical solutions to the Cauchy problem for a kind of quasilinear hyperbolic systems in divergence form
The authors consider the global existence of classical solution to a kind of second order quasilinear hyperbolic system subject to a null condition, with the linear elastodynamic system as its principal part and the nonlinear terms in divergence form depending on the product of \(u^2\) and the derivatives of \(u\). Basing on the fact that the nonlinear terms are of divergence form they obtained the generalized energy estimate for nonlocal energy. Using the generalized energy estimate they showed the global existence of classical solutions the considered Cauchy problem for small initial data.
scientific article; zbMATH DE number 5597533
scientific article