ПРЯМЫЕ И ОБРАТНЫЕ ЗАДАЧИ ДЛЯ УРАВНЕНИЙ СМЕШАННОГО ТИПА ЧЕТНОГО ПОРЯДКА

Аннотация

Subjects of research: direct and inverse problems for even-order equations and mixed-type equations of even order. Purpose of work: formulation and investigation of direct and inverse problems for even-order equations and mixed-type equations of even order. Methods of research: the method of a priori estimates, Fourier method, the theory of linear operators and the methods of functional analysis arc used. The results obtained and their novelty: - various new direct and inverse problems for even-order equations and mixed-type equations of even order arc formulated; - under certain conditions to given functions and in some problems depending on size of domain, the uniqueness and the existence of regular solution for those problems arc proved, the unique strong solvability of direct problems arc proved; - operator equations, which arc equivalent to considered problems arc studied and conclusion on a spectrum of the problems arc obtained; - a priory estimates for some problems, from which uniqueness and continuous dependence of regular solution from the right hand of the equation and existence of inverse operators arc obtained. Practical value: the results of the dissertation work have got theoretical character. Degree of embed and economic effectiveness: on the base of achieved results, the special course for the master-students can be teachcd and these results may be used in the subsequent theoretical development of this trend. Field of application: results of the dissertation can be used in the studying of boundary value problems for mixed type equations, in the further development of the theory of partial differential equations and at solving problems of mathematical physics which arc reducing to such equations.