Passports of specialty 01.01.02
01.01.00 – Mathematics (01.01.02 – Differential Equations, Dynamical Systems, and Optimal Control)
(Approved by the Resolution of the Presidium of the Supreme Attestation Commission under the President of the Republic of Tajikistan dated January 31, 2024, №41/шд)
SPECIALTY CODE: 01.01.02 – Differential Equations, Dynamical Systems, and Optimal Control
I. SCIENTIFIC FIELD FOR WHICH ACADEMIC DEGREES ARE AWARDED: Physical and Mathematical Sciences.
II. DEFINITION OF THE SPECIALTY: Differential Equations, Dynamical Systems, and Optimal Control is a branch of mathematical sciences focused on solvability and properties of solutions to ordinary differential equations, partial differential equations, functional-differential equations, finite difference equations, differential-operator equations, differential inequalities and inclusions, as well as properties of discrete, continuous, random, stochastic dynamical systems, and optimal control problems for differential equations and their systems. The primary scientific objectives of this specialty include investigating the solvability of differential equations, describing qualitative and quantitative properties of solutions, and exploring their applications.
III. RESEARCH AREAS:
1. General theory of differential equations and systems of differential equations.
2. Initial-boundary value problems and spectral problems for differential equations and systems of differential equations.
3. Qualitative theory of differential equations and systems of differential equations.
4. Nonlinear differential equations and systems of nonlinear differential equations.
5. Analytical theory of differential equations.
6. Theory of pseudodifferential operators.
7. Theory of differential-operator equations.
8. Theory of functional-differential equations.
9. Asymptotic theory of differential equations and systems.
10. Theory of differential inclusions and variational inequalities.
11. Differential equations and systems of differential equations in optimal control and calculus of variations.
IV. CODES AND NAMES OF RELATED SPECIALTIES:
01.01.01 – Real, Complex, and Functional Analysis; 01.01.03 – Mathematical Physics; 01.01.09 – Discrete Mathematics and Mathematical Cybernetics; 05.13.18 – Mathematical Modeling, Numerical Methods, and Software Complexes.
V. DISTINCTIONS FROM RELATED SPECIALTIES: Unlike specialty 01.01.02, specialty 01.01.01 (Real, Complex, and Functional Analysis) includes only works whose primary results characterize properties of special classes of functional spaces and special classes of operators arising from the study of differential equations.
Unlike specialty 01.01.03 (Mathematical Physics), specialty 01.01.02 includes works whose primary results concern properties of equations included in mathematical models of physical phenomena, but do not deal with the physical essence of processes described by these models.
Unlike specialty 01.01.09 (Discrete Mathematics and Mathematical Cybernetics), specialty 01.01.02 includes works dominated by ideas, approaches, and methods from the theory of differential, integral, integro-differential, and differential-operator equations.
Unlike specialty 05.13.18 (Mathematical Modeling, Numerical Methods, and Software Complexes), specialty 01.01.02 includes only works using mathematical models in the form of differential, finite difference, integral, integro-differential, and differential-operator equations, where the primary goal is obtaining rigorous mathematical results concerning the properties of the equations themselves within the considered models.