7 semester

1	Name of disciplines	Differential-operator equations (DOE)
2	Course of Study	4, specialty 1-31 03 01-04 Mathematics (research and development activities)
3	Semester of training	7
4	Amount of credits	5
5	Full name of lecturer	Doctor of Physical and Mathematical Sciences, Professor Lomovtsev Fedor Egorovich
6	Objectives of the study disciplines	Teach students to master the basic concepts of the theory of linear non-stationary differential-operator equations (DOE) with variable domains for determining unbounded operator coefficients and methods for investigating their correctness. As a result of the study, the student should be able to: – investigate the correctness of the Cauchy problem for parabolic and hyperbolic DOE; – illustrate them with mixed problems for equations of mathematical physics.
7	Prerequisites	Equations of mathematical physics, mathematical and functional analysis
8	Content disciplines	Basic concepts of linear partial differential equations (PDE) and DOE. Hadamard correctness of boundary value problems for DOE. Smooth, strong and weak solutions of the abstract Cauchy problem for parabolic (hyperbolic) DOE of the first (second) order with variable domains of definition of unbounded operators. Theorems on the existence, uniqueness, and increase of the smoothness of strong and weak solutions of the Cauchy problem. Correct mixed problems for hyperbolic and parabolic PDE with non-stationary boundary conditions.
9	Recommended literature	1. Tikhonov AN, Samarskii AA Equations of mathematical physics. Moscow, 2004. 2. Lomovtsev F.E. Boundary value problems for DOW with variable domains of definition of smooth and discontinuous operator coefficients. BSU. Doc. dis. 2002. 162 p.
10	Teaching Methods	Problematic, communicative with elements of educational and research activities.
11	Language of learning	Russian
12	Conditions (requirements), routine control	– laboratory and seminar classes, – preparation, presentation on the given topics.
13	Form of current certification	Offset