Open AccessOn the exterior Dirichlet-Neumann problem for the Biharmonic equation and its application in mechanics
Author(s) -
Hovik A. Matevossian
Publication year - 2020
Publication title -
iop conference series. materials science and engineering
Language(s) - English
Resource type - Journals
eISSN - 1757-899X
pISSN - 1757-8981
DOI - 10.1088/1757-899x/918/1/012099
Subject(s) - biharmonic equation , mathematics , uniqueness , dirichlet problem , dirichlet integral , bounded function , mathematical analysis , dirichlet distribution , neumann boundary condition , boundary value problem , uniqueness theorem for poisson's equation , dirichlet's principle , dirichlet's energy
We study the unique solvability of the mixed Dirichlet-Neumann biharmonic problem in the exterior of a compact set under the assumption that generalized solutions of this problem has a bounded Dirichlet (energy) integral with weight |x| a . Using the variational principle and depending on the value of the parameter a, we obtained uniqueness (non-uniqueness) theorems of the Dirichlet-Neumann problem or present exact formulas for the dimension of the space of solutions. The results of this paper are used in the study of mathematical problems in mechanical models, in particular, in transport models and procedures.