Mohammad El Smaily (Associate Professor)
BSc (Lebanese University), MSc (Lebanese University), PhD (Aix-Marseille)
My research interests lie in nonlinear analysis, partial differential equations (PDEs) and dynamical systems. This mathematical analysis aims ultimately to describe population dynamics, invasion phenomena in heterogeneous media, as well as optimal strategies for mixing in diffusive and/or reactive media. In more precise words, I am interested in deterministic studies of elliptic and parabolic PDEs, nonlinear evolution equations and the wave propagation aspects related to these models. Other areas of special interest are semi-linear wave equations with connections to the evolution of minimal surfaces in Minkowski space and topological defects.
The math toolbox in my work is based on techniques from functional and spectral analysis, fixed point theory, elliptic/parabolic/hyperbolic PDEs, calculus of variations, and measure theory.
My current work involves:
• Traveling fronts and propagation phenomena for Reaction-Advection-Diffusion equations in heterogenous media
• Population dynamics and biological invasion models
• Fluid dynamics and mixing
• Elliptic and parabolic non-linear partial differential equations: qualitative properties and classification of solutions
• Defects in semi-linear wave equations and time-like minimal surfaces