MARKO ERCEG
Associate professor at the Departmant of Mathematics, Faculty of Science, University of Zagreb.
Research interest
PDEs and functional analysis: microlocal analysis (semiclassical measures, H-measures and variants), Friedrichs systems, degenerate parabolic equations, operator theory.
Teaching
Introduction to optimization, Methods in mathematical physics, Nonlinear analysis II, Mathematics (for molecular biologists)
G-convergence of Friedrichs systems revisited
We revisit homogenisation theory for Friedrichs systems. In particular, we show that G-compactness can be obtained under severely weaker assumptions than in the original work of Burazin and Vrdoljak (2014). In this way we extend the applicability of G-compactness results for Friedrichs systems to equations that yield memory effects in the homogenised limit. [Read more]
Degenerate parabolic equations -- compactness and regularity of solutions
We introduce a new method which resolves the problem of regularity and compactness of entropy solutions for nonlinear degenerate parabolic equations under non–degeneracy conditions on the sphere. The method of proof is reduction of the equation to a specific kinetic formulation involving two transport equations, one of the second and one of the first order. [Read more]
