Recent Advances in Nonlinear PDEs

Department of Mathematics, IIT Madras

13-15 March, 2025

A brief overview of the conference

Nonlinear partial differential equations (PDEs) form an important branch of mathematical physics that finds applications in various fields of science and technology, such as continuum mechanics, hydrodynamics, quantum mechanics, biophysics, and others. The study of nonlinear PDEs allows us to understand the physical processes occurring in nature better and develop new methods for their description and analysis.

The conference “Recent advances in nonlinear PDEs” will be a significant event in the scientific world. It will bring together leading experts worldwide (India, USA, Europe, Middle East) who will present their latest achievements. This will allow participants to exchange ideas, discuss current issues, and identify new research directions.

Our conference will allow young researchers to get acquainted with advanced methods for studying nonlinear PDEs, establish contacts with leading scientists, and get valuable advice on developing their research projects. The event will strengthen scientific ties between IIT Madras and other universities and research centres, leading to further cooperation and development of research at IITM and strengthening its reputation as a centre of excellence in mathematics and physics.

Principal themes of the conference

Qualitative Theory of Nonlinear PDEs

Existence and uniqueness of solutions to quasilinear, semi-positone, non-Lipschitz, and other classes of elliptic and parabolic equations. Properties of solutions related to smoothness, regularity, symmetries, and asymptotic behaviour.

Variational and Topological Methods of nonlinear analysis

Their development and application in differential equations and nonlinear spectral theory by studying critical points of functionals and fixed points of operator mappings.

Functional Inequalities

Estimates, stability, attainability of best constants, properties of extremal functions, connections with rearrangement theory, and applications in spectral optimization problems and the theory of PDEs.