This five-day workshop is devoted to advanced and contemporary research developments in Partial Differential Equations (PDEs), with emphasis on both rigorous analytical frameworks and emerging interdisciplinary directions. The programme will focus on deep structural aspects of PDE theory, including variational methods, regularity theory, non-divergence form equations, viscosity solutions, hyperbolic conservation laws, nonlinear phenomena, and modern techniques in numerical analysis.
Special attention will be given to fully nonlinear equations, weak and strong solution frameworks, stability analysis, and the interplay between elliptic, parabolic, and hyperbolic structures. The workshop will also explore PDE-driven mathematical modeling arising in continuum mechanics, fluid dynamics, population dynamics, and other applied domains, along with computational perspectives that connect analysis and simulation.
Designed for researchers, faculty members, and doctoral scholars from premier institutes, the workshop aims to foster high-level academic interaction, stimulate discussion on open problems, and encourage long-term research collaborations. By bringing together experts from diverse subfields, the programme seeks to provide participants with a comprehensive view of current research trends and future directions in PDE theory and its applications.

• Variational Methods and Nonlinear Elliptic PDEs
  Weak solution frameworks, direct methods in the calculus of variations, critical point theory, regularity theory, and qualitative properties of nonlinear elliptic equations.

• Non-divergence Form Equations and Viscosity Solutions
  Fully nonlinear elliptic and parabolic equations, comparison principles, stability theory, Pucci extremal operators, Hamilton–Jacobi equations, and connections to optimal control and HJB frameworks.

• Hyperbolic PDEs and Conservation Laws
  Well-posedness theory, entropy solutions, shock formation, wave propagation phenomena, and stability analysis for nonlinear hyperbolic systems.

• Numerical Methods for PDEs
  Finite element and finite difference methods, stability and convergence analysis, discretization of nonlinear problems, and computational challenges in high-dimensional settings.

• Mathematical Modeling Perspectives
  PDE models arising in fluid mechanics, continuum mechanics, population dynamics, and interdisciplinary applications, emphasizing the interplay between modeling, analysis, and computation.

Registration Fee: NIL
Selection based on academic background. No TA provided.
Apply via Google Form: https://forms.gle/AHiQZdvhHAp79bRU7

• Last Date for Registration: 24 February 2026
• Intimation of Selection: 25 February 2026
• Workshop Dates: 13–17 March 2026

For details and updates: https://vnit.ac.in/basic science/maths/workshop

For communication:

Email: pdeworkshop.vnit2026@mth.vnit.ac.in

Mobile No: +91-9444378326