On the exterior Dirichlet-Neumann problem for the Biharmonic equation and its application in mechanics
Hovik A. Matevossian · IOP Conference Series Materials Science and Engineering · 2020
Abstract 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.