Professor Sergey Mikhailov
Professor - Applied Mathematics and Analysis

Research area(s)

Applied Analysis, Solid Mechanics, and Computational Mathematics, including:

• Analysis of Stokes, Oseen, and Navier-Stokes PDEs, especially of existence, uniqueness and regularity of solution of evolution (non-stationary) problems in Sobolev spaces.
• Boundary-domain integral and integro-differential equations.
• Theoretical fatigue, damage, durability, and fracture mechanics.
• Nonlinear partial integro-differential Volterra equations of crack propagation in damaged media.

Project details

• Mathematical Analysis of Localised Boundary-Domain Integral Equations for Nonlinear PDEs, funded by the Engineering and Physical Sciences Research Council (EPSRC), EP/M013545/1, 2015-2018.
• Mathematical Analysis of Localised Boundary-Domain Integral Equations for BVPs with Variable Coefficients, funded by the Engineering and Physical Sciences Research Council (EPSRC), EP/H020497/1, 2010-2013.
• Boundary-Domain Integral and Integro-Differential Equations: Formulation, Analysis, Localisation, funded by the Royal Society, 2006-2009.
• Analysis of Boundary-Domain Integral and Integro-Differential Equations, funded by the London Mathematical Society and Nuffield Foundation, 2006-2008.
• Nonlinear Dynamics and Rock Contact Fracture Mechanics in Modelling of Vibration Enhanced Drilling, funded by the Engineering and Physical Sciences Research Council (EPSRC), 2002-2006. 
• Non-Local Approach to High Cyclic Fatigue: Theoretical Basis, funded by the Engineering and Physical Sciences Research Council (EPSRC), 1999-2001