The use of conservation laws for solving boundary value problems of the Moisila—Teodorescu system

The Moisil—Teodorescu system is a three-dimensional analogue of the Cauchy—Riemann system of equations and is related to the spatial static Lame equations. Many works have investigated these equations. Analogs of many results known for the Cauchy—Riemann equations in these papers are obtained. Solutions of the Moisila—Teodorescu system preserve many properties of analytical functions of a complex variable. In our work, some exact solutions of this system are constructed and an infinite series of new conservation laws for the equations of the Moisil—Teodorescu system is given. These laws are linear in derivatives. We have constructed the laws used to solve the boundary value problems of the Moisila—Teodorescu system.