International Journal of Differential Equations
Volume 2010 (2010), Article ID 464251, 10 pages
Research Article

On Mixed Problems for Quasilinear Second-Order Systems

via Millaures, 12–10146 Turin, Italy

Received 20 May 2010; Revised 4 August 2010; Accepted 30 August 2010

Academic Editor: Bashir Ahmad

Copyright © 2010 Rita Cavazzoni. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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 d. 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 vHs(d+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.