We study the some properties of solutions of biharmonic problems. Namely, we study the boundary value problems Navier and Neumann for the biharmonic equation. For solving these biharmonic problems with application we need to solve boundary value problems Dirichlet and Cauchy for the Poisson equation using the scattering model. In order to select suitable solutions, we solve the Poisson equation with the corresponding boundary conditions, that is, some criterion function is minimized in the Sobolev norms. Under appropriate smoothness assumptions, these problems may be reformulated as boundary value problems for the biharmonic equation. The results of this paper are used to study mathematical problems in mechanical models using computational approaches, in particular, their application in advanced technologies in the aerospace and mechanical engineering, as well as in advances in materials science.

Biharmonic Navier and Neumann Problems and Their Application in Mechanical Engineering

G. Nordo
Penultimo
Investigation
;
2021-01-01

Abstract

We study the some properties of solutions of biharmonic problems. Namely, we study the boundary value problems Navier and Neumann for the biharmonic equation. For solving these biharmonic problems with application we need to solve boundary value problems Dirichlet and Cauchy for the Poisson equation using the scattering model. In order to select suitable solutions, we solve the Poisson equation with the corresponding boundary conditions, that is, some criterion function is minimized in the Sobolev norms. Under appropriate smoothness assumptions, these problems may be reformulated as boundary value problems for the biharmonic equation. The results of this paper are used to study mathematical problems in mechanical models using computational approaches, in particular, their application in advanced technologies in the aerospace and mechanical engineering, as well as in advances in materials science.
2021
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11570/3207458
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