【Plenary Lecture】Entropy Analysis and Singularities of Solutions for Nonlinear Hyperbolic Conservation Laws

Speaker: Prof. Gui-Qiang C. Chen (University of Oxford)

Title:  Entropy Analysis and Singularities of Solutions for Nonlinear Hyperbolic Conservation Laws

Abstract:  In this talk, we present some reflections and recent developments in solving several longstanding open problems involving the singularities of entropy solutions for nonlinear hyperbolic conservation laws and related nonlinear partial differential equations through entropy analysis and associated methods. These problems especially include the minimal entropy conditions for well-posedness, the understanding of the phenomena of cavitation/decavitation and concentration/deconcentration, and the rigorous analysis for entropy solutions via the theory of divergence-measure fields, among others. Further related topics, perspectives, and open problems will also be addressed.