Investigation of hyperbolic systems with order degeneration arising in I. Vekua's hierarchical models

Abstract

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.

Keywords:

• elastic prismatic shell
• cusped prismatic shell
• hierarchical models
• dynamical problems
• order-degenerating hyperbolic system
• weak solution
• strong solution
• a priori estimate
• galerkin method

AMS Subject Classifications::

• 74K20
• 35L53
• 35L80

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Erratum

Acknowledgements

This research was supported by the Georgian Technical University grant No. GTU/2011/4.