Метод энергетических неравенств и операторов осреднения

Abstract

At the beginning of the article it is giving a short description of the development of Solvability Theory of Boundry Problems for Partial Linear Differential Equations with using of functional methods. After this general results on the base of energetic inequalities are stated. At the second part of the article it is proven the existence and uniqueness of a strong solution of boundary problems for hyperbolic about given vector field differential equation of the 2-nd order using method of energetic inequalities and averaging operators with variable step. Energetic inequality is derived using Silvester criteria for quadric forms