Open AccessESTIMATES OF THE EIGENVALUES AND EIGENFUNCTIONS OF OPERATOR ARISING IN SWELLING PRESSURE MODEL
Author(s) -
Zh.A. Kaiyrbek,
G. Auzerkhan,
Lyaylya Kurmantaevna Zhapsarbaeva
Publication year - 2020
Publication title -
habaršy. fizika-matematika seriâsy
Language(s) - English
Resource type - Journals
ISSN - 1728-7901
DOI - 10.51889/2020-3.1728-7901.08
Subject(s) - eigenfunction , eigenvalues and eigenvectors , boundary value problem , operator (biology) , nonlinear system , mathematical analysis , mathematics , instability , euler's formula , physics , mechanics , chemistry , biochemistry , repressor , quantum mechanics , transcription factor , gene
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.