Numerical investigation of the non-uniqueness of solutions of the Showalter–Sidorov problem for the Hoff mathematical model on a rectangle

The article is devoted to the question of the uniqueness or non-uniqueness of solutions of the Showalter–Sidorov–Dirichlet problem for the Hoff equation on a rectangle. To study this issue, the phase space method was used, which was developed by G.A. Sviridyuk. An algorithm is constructed to identify the conditions of multiplicity and uniqueness of solutions, which allows numerically solving the Showalter–Sidorov–Dirichlet problem based on the modified Galerkin method. The article considers cases where the dimension of the operator kernel with a time derivative is equal to 1 or 2. Computational experiments demonstrating the non-uniqueness of solutions to the Showalter–Sidorov problem depending on the values of the problem parameters are presented.