The uniform convergence of the eigenfunctions expansions of the biharmonic operator in closed domain

The mathematical models of the various vibrating systems are partial differential equations and finding the solutions of such equations are obtained by developing the theory of eigenfunction expansions of differential operators. The biharmonic equation which is fourth order differential equation is encountered in plane problems of elasticity. It is also used to describe slow flows of viscous incompressible fluids. Many physical process taking place in real space can be described using the spectral theory of differentiable operators, particularly biharmonic operator. In this paper, the problems on the uniform convergence of eigenfunction expansions of the functions from Nikolskii classes corresponding to the biharmonic operator are investigated.