Speaker
Description
The concept of positive symmetric systems, also known as Friedrichs systems, originated with Kurt Otto Friedrichs in 1958. He demonstrated that this framework encompasses a broad range of initial and boundary value problems for various types of linear partial differential equations. Renewed interest in these systems emerged from advancements in the numerical analysis of differential equations, particularly with the development of abstract Friedrichs systems in Hilbert spaces by Ern, Guermond, and Caplain in 2007. Over the past two decades, the theory has been extensively explored from both theoretical and numerical perspectives, including the homogenization theory for Friedrichs systems introduced by Burazin and Vrdoljak in 2014.
A connection between m-accretive extensions of Friedrichs operator and extensions "with signed boundary map" shall be presented. Then, for such extensions the revisited homogenization theory shall be presented in which we demonstrate that G-compactness can be achieved under significantly weaker conditions than those required in the original study by Burazin and Vrdoljak (2014). This extension broadens the applicability of G-compactness results to equations that exhibit memory effects in the homogenized limit while circumventing the use of compactness techniques employed in earlier approaches.
