International Journal of Differential Equations
- Int. J. Differ. Equ.
- Volume 2010 (2010), Article ID 464251, 10 pages.
On Mixed Problems for Quasilinear Second-Order Systems
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.
Int. J. Differ. Equ., Volume 2010 (2010), Article ID 464251, 10 pages.
Received: 20 May 2010
Revised: 4 August 2010
Accepted: 30 August 2010
First available in Project Euclid: 26 January 2017
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Cavazzoni, Rita. On Mixed Problems for Quasilinear Second-Order Systems. Int. J. Differ. Equ. 2010 (2010), Article ID 464251, 10 pages. doi:10.1155/2010/464251. https://projecteuclid.org/euclid.ijde/1485399924