Timoshenko equation

The Cauchy-Poisson method is extended to n-dimensional Euclidean space so that to obtain partial differential equations (PDEs) of a higher order.   The application in the construction of hyperbolic approximations is presented, generalizing and supplementing the previous investigations.   Restrictions on derivatives in Euclidean space are introduced.  The hyperbolic degeneracy by parameters and its realization in the form of necessary and sufficient conditions are considered.  As a particular case of 4-dimensional Euclidean space, keeping operators up to the 6th order, we obtain a generalize