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Abstract We study a two-dimensional boundary value problem described by a tensorial equation in a bounded domain. Once its more general definition is given, we conclude that its analysis is linked to the resolution of an overdetermined hyperbolic problem and hence present some discussions and considerations. Secondly, for a simplified version of the original formulation, which leads to a degenerate problem on a rectangle, we prove the existence and uniqueness of a solution under proper assumptions on the data.