Numerical investigation of eigenoscillations near the system of two strips forming a cross in the channel

The existence of eigenoscillations near the system mentioned in the title system is proven. The number of oscillation modes is determined. A classification by groups of possible symmetry is carry out. An infinite matrix equation for the coefficients of corresponding expansion is obtained. This equation is investigated numerically. The plots of eigenvalues versus the length of the cross are obtained. An approximate formula for the eigenvalues is found and investigated. The theory of the self-adjoint operators, the "Dirichlet-Neumenn bracket" and variational methods are used.