Rafael A Monteiro Da Silva

Biography

Rafael A Monteiro da Silva is a Postdoctoral Researcher at the Mathematics for Advanced Materials - Open Innovation Laboratory (MathAm-OIL)

Research Interest

My research focuses on the use of infinite dimensional dynamical systems techniques in Partial Differential Equations (PDEs). During my PhD my research focused on bifurcations in hyperbolic-parabolic partial differential equations and associated bifurcation phenomena. In particular, I studied the interplay between viscous and inviscid stability criteria through Evans and Lopatinski conditions in the context of magnetohydrodynamics. More recently, I have been studying pattern formation in reaction diffusion equations, leaning towards a ”spatial dynamics perspective” rather than relying on the techniques I used before; I believe this new perspective to be the most appropriate in some contexts. I have also looked for a more functional analytic approach to multidimensional patterns, which relies on matching techniques, asymptotic analysis and broad tools from both PDE and spectral theory; roughly speaking, the main goal consists in avoiding one dimensional dynamical systems techniques, building new machinery to deal with higher dimensional phenomena