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2010 On Mixed Problems for Quasilinear Second-Order Systems
Rita Cavazzoni
Int. J. Differ. Equ. 2010: 1-10 (2010). DOI: 10.1155/2010/464251


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.


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Rita Cavazzoni. "On Mixed Problems for Quasilinear Second-Order Systems." Int. J. Differ. Equ. 2010 1 - 10, 2010.


Received: 20 May 2010; Revised: 4 August 2010; Accepted: 30 August 2010; Published: 2010
First available in Project Euclid: 26 January 2017

zbMATH: 1206.35150
MathSciNet: MR2727998
Digital Object Identifier: 10.1155/2010/464251

Rights: Copyright © 2010 Hindawi


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