Biharmonic equation

The thesis proposes a simple but very effective method to study the unique solvability and an iterative method for solving five boundary value problems for nonlinear fourth order ordinary differential equations with different types of boundary conditions and two boundary value problems for a biharmonic equation and a biharmonic equation of Kirchhoff type by using the reduction of these problems to the operator equations for the function to be sought or an intermediate function.

27p larachdumlanat129 20-01-2021 25 2   Download

The method is developed for plates on internal supports of more complex configurations. Namely, we examine the cases of symmetric rectangular and H-shape supports, where the computational domain after reducing to the first quadrant of the plate is divided into three subdomains. Also, we consider the case of asymmetric rectangular support where the computational domain needs to be divided into 9 subdomains. The problems under consideration are reduced to sequences of weak mixed boundary value problems for the Poisson equation, which are solved by difference method.

14p 12120609 23-03-2020 19 1   Download

In this paper we study a boundary value problem for a nonlinear biharmonic equation, which models a bending plate on nonlinear elastic foundation. We propose a new approach to existence and uniqueness and numerical solution of the problem.

17p thuyliebe 05-10-2018 32 1   Download