Quasilinear Anisotropic Degenerate Parabolic Equations: Continuous Dependence Estimates and Renormalized Entropy Solutions

Dr. Kenneth Karlsen

Professor of Mathematics
University of Bergen, Norway

Abstract:  This talk will consist of three parts:

1. A short overview of recent development in entropy solution theory for quasi-linear degenerate parabolic equations possessing discontinuous solutions.
2. Present a $L^1\cap L^\infty$ framework for deriving continuous dependence and error estimates, along with some applications. This is joint work with Gui-Qiang Chen.
3. Present a pure $L^1$ well-posedness theory based on renormalized entropy solutions. This is based on joint work with Mostafa Bendahmane.