Analysis of differential and pseudodifferential problems of mixed type
Partial differential equations (PDEs) model a wide range of phenomena in physics, biology, and geoscience. Their classification into hyperbolic, parabolic, and elliptic types plays a central role in analysis. Many important problems, however, involve equations of mixed type, where different behaviours coexist; for example in flows transitioning from subsonic to supersonic regimes. Such equations are particularly challenging due to the interaction of opposing analytical properties.
This project studies mixed-type and degenerate equations within two classical frameworks: the kinetic formulation of degenerate parabolic equations and Friedrichs systems. Our aim is to obtain new results on fundamental questions including well-posedness, regularity, and boundary behaviour. By combining tools from microlocal and harmonic analysis with structural insights from these frameworks, we seek a systematic understanding of equations of mixed type.
Email: marko.erceg (at) math.hr
Department of Mathematics, Faculty of Science, University of Zagreb, Croatia