Abstract
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 , with , is proved in the case where is a half-space of . 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 and through a function . 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.
Citation
Rita Cavazzoni. "On Mixed Problems for Quasilinear Second-Order Systems." Int. J. Differ. Equ. 2010 1 - 10, 2010. https://doi.org/10.1155/2010/464251
Information