A characterization of the solutions of the darboux problem for third order hyperbolic inclusions

Georgeta Teodoru

Department of Mathematics, Technical University "Gh. Asachi" Iaşi, Iaşi, România

Abstract: In this paper we consider the Darboux Problem for a third order hyperbolic inclusion of the form $u_{xyz}\in F (x,y,z,u)$ and we prove a characterization of the solutions of the considered problem using the Aumann integral defined for multifunctions.

Keywords and phrases: Multifunction, hyperbolic inclusion, upper semi-continuity, initial values, absolutely continuous in Carathéodory's sense function, Aumann integral.

MSC: 35L30, 35R70, 47H10

Received: 04.10.2006

Language: English

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