Passports of specialty Doctor of Philosophy (PhD) – Specialty Doctor 6D060100 – Mathematics
(6D060102 – 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:
6D060102 – Differential Equations, Dynamical Systems, and Optimal Control (PhD program)
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 an area of mathematical science that focuses on the 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 are investigating the solvability of differential equations, describing qualitative and quantitative characteristics of solutions, and their applications.
III. AREAS OF RESEARCH:
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 pseudo-differential 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 variational calculus problems.
IV. RELATED SPECIALTY CODES AND NAMES:
6D060101 – Real, Complex, and Functional Analysis;
6D060103 – Mathematical Physics;
6D060109 – Discrete Mathematics and Mathematical Cybernetics;
6D070502 – Mathematical Modeling, Numerical Methods, and Software Complexes.
V. DISTINCTIONS FROM RELATED SPECIALTIES:
- Unlike specialty 6D060102, specialty 6D060101 (Real, Complex, and Functional Analysis) covers 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 6D060103 (Mathematical Physics), specialty 6D060102 includes works whose primary results pertain to properties of equations forming mathematical models of physical phenomena but do not consider the physical essence of processes described by these models.
- Unlike specialty 6D060109 (Discrete Mathematics and Mathematical Cybernetics), specialty 6D060102 includes works dominated by ideas, approaches, and methods from the theory of differential, integral, integro-differential, and differential-operator equations.
- Unlike specialty 6D070502 (Mathematical Modeling, Numerical Methods, and Software Complexes), specialty 6D060102 includes only works using mathematical models in the form of differential, finite-difference, integral, integro-differential, and differential-operator equations, primarily aiming at obtaining rigorously justified mathematical results concerning the properties of the equations themselves within the models considered.