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We study the well-posedness of an initial-boundary value problem corresponding to the zeroth approximation of I. Vekua's hierarchical models for elastic cusped prismatic shells. The mathematical model is described by a two-dimensional order-degenerating hyperbolic system. We formulate the problem in the weak setting and prove the uniqueness and existence theorems. We show that the sequence of corresponding explicit Galerkin approximations converges to the exact solution in an appropriate weighted Lebesgue space.
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