ESTIMATES OF THE EIGENVALUES AND EIGENFUNCTIONS OF OPERATOR ARISING IN SWELLING PRESSURE MODEL - Kaiyrbek Ж.; Auzerkhan Г.; Zhapsarbaeva Л.Қ (Bulletin of Abai KazNPU. Series of Physical and Mathematical sciences, 2020)
Swelling forces from materials confined by structures can cause structural deformations and instability. Due to the complexity of interactions between expansive solid and solid-liquid equilibrium, the forces exerting on retaining structures from swelling are highly nonlinear. This work is our initial attempt to study a simplistic initial/boundary value problem based on the Euler-elastic beam theory and some swelling force model. In this paper, we study a nonlinear problem for the equation of a beam. The self-adjointness of the operator corresponding to the nonlinear problem for the Euler equations is proved. Two-sided estimates of the eigenvalues of the operator in question are established. Two-sided estimates of the eigenfunctions of the operator of the initial-boundary value problem for the beam equation are also obtained.