On Mixed Problems for Quasilinear Second-Order Systems

الملخص EN

The paper is devoted to the study of initial-boundary value problems for quasilinear second-order systems.

Existence and uniqueness of the solution in the space Hs(Ω¯×[0,T]), with s>d/2+3, is proved in the case where Ω is a half-space of ℜd.

The proof of the main theorem relies on two preliminary results: existence of the solution to mixed problems for linear second-order systems with smooth coefficients, and existence of the solution to initial-boundary value problems for linear second-order operators whose coefficients depend on the variables x and t through a function v∈Hs(ℜd+1).

By means of the results proved for linear operators, the well posedness of the mixed problem for the quasi-linear system is established by studying the convergence of a suitable iteration scheme.