Biharmonic Navier and Neumann problems and their application in mechanical engineering

DOI10.1134/S1995080221080199zbMath1473.35180OpenAlexW3168250525MaRDI QIDQ1982471

H. A. Matevossian, A. R. Ulukhanyan, M. U. Nikabadze, Giorgio Nordo

Publication date: 8 September 2021

Published in: Lobachevskii Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s1995080221080199

zbMATH Keywords

boundary value problemsvariational methodsbiharmonic operator

Mathematics Subject Classification ID

Boundary value problems for higher-order elliptic equations (35J40) Variational methods applied to PDEs (35A15) Biharmonic and polyharmonic equations and functions in higher dimensions (31B30) Higher-order elliptic equations (35J30)

Related Items

Biharmonic Fick-Jacobs diffusion in narrow channels

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On solutions of the Neumann problem for the biharmonic equation in unbounded domains
• On solutions of a boundary value problem for the biharmonic equation
• Polyharmonic boundary value problems. Positivity preserving and nonlinear higher order elliptic equations in bounded domains
• An eigenvalue problem for tensors used in mechanics and the number of independent Saint-Venant strain compatibility conditions
• On the Steklov-type biharmonic problem in unbounded domains
• On solutions of the exterior Dirichlet problem for the biharmonic equation with a finite weighted Dirichlet integral.
• On the biharmonic problem with the Steklov-type and Farwig boundary conditions
• On the decomposition of equations of micropolar elasticity and thin body theory
• On the problem of eigenvalues of material tensor objects and wave velocities
• On solutions of the mixed Dirichlet-Steklov problem for the biharmonic equation in exterior domains
• Topics on tensor calculus with applications to mechanics
• Estimates for solutions of the Dirichlet problem for the biharmonic equation in a neighbourhood of an irregular boundary point and in a neighbourhood of infinity. Saint-Venant's principle
• On the polyharmonic Neumann problem in weighted spaces
• A note on the Neumann eigenvalues of the biharmonic operator
• The Influence of Poisson’s Ratio on the Vibrational Spectrum