NUMERICAL STUDY OF THE NON-UNIQUENESS OF SOLUTIONS TO THE SHOWALTER-SIDOROV PROBLEM FOR A MATHEMATICAL MODEL OF I-BEAM DEFORMATION

Abstract

The article is devoted to the question of the uniqueness or multiplicity of solutions of the Showalter-Sidorov-Dirichlet problem for the Hoff equation on a segment. The Hoff equation simulates the dynamics of deformation of an I-beam under constant load. To investigate the non-uniqueness of solutions to the Showalter-Sidorov problem, the phase space method will be used, which was developed by G.A. Sviridyuk to study the solvability of Sobolev-type equations. It was also previously shown that the phase space of the model under study contains features of type 2-Whitney assembly. The article presents the conditions of uniqueness or multiplicity of solutions to the Showalter-Sidorov problem depending on the system parameters. An algorithm for the numerical solution of the problem based on the Galerkin method. The results of computational experiments are presented.