Abstract
Some overdetermined problems, formulated for the Laplace equation in a circle (for arbitrary class of functions, not necessarily analytical) and a half-plane, the heat equation, the one-dimensional wave equation, the elasticity equations for planar deformation, the plasticity and deformations theory problem for a plane with a circular hole, dynamic elasticity theory problems for a half-plane and a half-space with simultaneously known on one its boundary the Dirichlet condition, and the Neumann condition are investigated. Analytical and numerical solutions are constructed, stress-strain states, thermal and other states are restored, internal structure of the body, concentrated sources are determined.
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