Hyperbolic Problems: Theory, Numerics, and Applications

This volume presents a comprehensive overview of recent developments in the theory, numerical analysis, and applications of hyperbolic partial differential equations, bringing together contributions spanning fundamental mathematical theory, computational methods, and interdisciplinary applications.Topics covered include structure-preserving and high-order numerical methods, the transition from viscous to discontinuous solutions in compressible flows, random and statistical approaches to the compressible Euler equations, quantum simulation of partial differential equations, and the stability of shear flows, alongside quantum and relativistic hydrodynamics, multiphase flow methods, radiation hydrodynamics, transonic and hypersonic flows, shallow water and tsunami modeling, boundary stabilization, and inverse problems.The volume is based on selected papers presented at the 19th International Conference on Hyperbolic Problems: Theory, Numerics, and Applications (HYP 2024), held at Shanghai Jiao Tong University, Shanghai, China, during July 1–5, 2024. Held every two years since its inception in France in 1986, the HYP conference series brings together researchers working on hyperbolic partial differential equations through plenary, invited, and contributed talks, and features the James Glimm Lecture as well as the presentation of the Peter Lax Award recognizing outstanding early-career contributions to the field.