Numerical study of the non-uniqueness of solutions to the Showalter–Sidorov problem for a mathematical model of I-beam deformation

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.