On Some Problems Generated by a Sesquilinear Form

Abstract

Based on the generalized Green formula for a sesquilinear nonsymmetric form for the Laplace operator, we consider spectral nonself-adjoint problems. Several such problems are similar to classical ones; others arise in problems of hydrodynamics and diffraction and in problems with surface dissipation of energy. Properties of solutions of such problems are considered. Also, we study initialboundary value problems generating the considered spectral problems and prove correct solvability theorems for such problems on any interval of time.