On Mixed Problems for Quasilinear Second-Order Systems

Rita Cavazzoni

International Journal of Differential Equations, 2010, vol. 2010, 1-10

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 ð » ð ‘ ( Ω × [ 0 , 𠑇 ] ) , with ð ‘ > ð ‘‘ / 2 + 3 , is proved in the case where Ω is a half-space of â„œ ð ‘‘ . 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 ð ‘¥ and ð ‘¡ through a function ð ‘£ ∈ ð » ð ‘ ( â„œ ð ‘‘ + 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.

Date: 2010
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnijde:464251

DOI: 10.1155/2010/464251

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