Explore the programs and courses offered by Partial differential equations
Browse Programs Admission InformationThe doctoral program in Partial Differential Equations (PDEs) aims to train highly qualified researchers in this fundamental branch of mathematical analysis and applied mathematics. It offers deep theoretical understanding of PDEs, mastery of advanced analytical and numerical tools, and the development of research skills necessary to solve complex problems arising in physics, engineering, biology, and data science. The program also encourages interdisciplinary and international research collaborations.
Advanced Partial Differential Equations
In-depth study of elliptic and parabolic PDEs.
Functional Analysis
Hilbert and Banach spaces, linear operators, duality, and compactness.
Sobolev Spaces and Applications
Study of Sobolev spaces, inequalities, and embedding theorems.
Variational Methods
Analysis of weak solutions using variational principles and energy functionals.
Numerical Analysis of PDEs
Numerical methods such as finite differences, finite elements, and stability analysis.
Mathematical Modeling
Application of PDEs to model physical, biological, and engineering phenomena.
Research Seminar
Presentation and discussion of recent scientific articles within a research group.
Nonlinear PDEs and Qualitative Analysis
Study of existence, blow-up, and long-term behavior of solutions.
Regularity Theory
Investigation of the smoothness of solutions, especially under irregular data or domains.
Optimal Control and PDEs
Application of control theory to systems governed by PDEs.
Spectral Analysis
Study of eigenvalues and eigenfunctions of differential operators.
Nonlocal PDEs
PDEs involving integral operators or fractional derivatives.
PDEs on Irregular Domains
Analysis of solutions in geometrically complex or non-smooth domains.