In the present paper static and dynamical one-dimensional models for elastic rods are constructed. The existence and uniqueness of solutions to the corresponding boundary and initial boundary value problems are proved, the rate of approximation of the solutions to the original three-dimensional problems by vector-functions restored from the solutions of one-dimensional problems is estimated.
"On the construction and investigation of hierarchic models for elastic rods." Hiroshima Math. J. 36 (3) 365 - 386, November 2006. https://doi.org/10.32917/hmj/1171377079