Biharmonic Problems and their Applications in Engineering and Technology

In the present paper we study some properties of solutions of biharmonic problems. Namely, we study the Steklov, Steklov-type and Neumann boundary value problems for the biharmonic equation. For solving these biharmonic problems with application, in particular, to radar imaging, we need to solve the Dirichlet, Neumann and Cauchy boundary value problems for the Poisson equation using the scattering model. In order to select suitable solutions, we solve the Poisson equation with the corresponding boundary conditions, that is, some criterion function is minimized in the Sobolev norms. Under appropriate smoothness assumptions, these problems may be reformulated as boundary value problems for the biharmonic equation.