International Journal of Differential Equations

On Mixed Problems for Quasilinear Second-Order Systems

Rita Cavazzoni

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 ${H}^{s}(\overline{\Omega }\times[0,T])$, with $s>d/2+3$, is proved in the case where $\Omega$ is a half-space of ${\Re }^{d}$. 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 $v\in {H}^{s}({\Re }^{d+1})$. 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.

Article information

Source
Int. J. Differ. Equ., Volume 2010 (2010), Article ID 464251, 10 pages.

Dates
Revised: 4 August 2010
Accepted: 30 August 2010
First available in Project Euclid: 26 January 2017

https://projecteuclid.org/euclid.ijde/1485399924

Digital Object Identifier
doi:10.1155/2010/464251

Mathematical Reviews number (MathSciNet)
MR2727998

Zentralblatt MATH identifier
1206.35150

Citation

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

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