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Intro; Contents; Proceedings of the 16th International Conference on Hyperbolic Problems: Theory, Numerics and Application; Organizer's Introduction; Reference; Speakers at the 16th International Conference on Hyperbolic Problems that Contributed to these Proceedings; The Sharp-Interface Limit for the Navier-Stokes-Korteweg Equations; 1 Introduction; 2 A Priori Estimates and Compactness Properties; 3 The Sharp-Interface Limit and Main Theorem; 4 Conclusions; References; Asymptotic Behavior of a Solution of Relaxation System for Flow in Porous Media; 1 Introduction
2 Physical and Mathematical Models2.1 Mathematical Analysis; 3 Numerical Experiments; 4 Concluding Remarks; References; Optimal Control of Level Sets Generated by the Normal Flow Equation; 1 Introduction; 2 Optimal Control of Level Set Dynamics; 3 Approximate Solutions with the Extended Ritz Method; 4 Adjoint Equation and Optimization Procedure; 5 Simulation Results; 6 Conclusions; References; Emergent Dynamics for the Kinetic Kuramoto Equation; 1 Introduction; 1.1 The Kuramoto Model for N Oscillators; 1.2 The Kinetic Kuramoto Equation; 2 BV Solutions and the Front-Tracking Algorithm
2.1 Identical Oscillators2.2 Nonidentical Oscillators; 3 Phase Concentration of the Kuramoto-Sakaguchi Equation; 3.1 Identical Oscillators; 3.2 Nonidentical Oscillators; References; A Hyperbolic Model of Nonequilibrium Phase Change at a Sharp Liquid-Vapor Interface; 1 Context; 2 Mathematical Model; 2.1 Conservation Equations; 2.2 Hyperbolicity; 2.3 Comparison with Other Models; 2.4 Limitation; 3 Discretization and Test Cases; 3.1 Discretization Strategy; 3.2 Numerical Results; 4 Conclusion; References; The Cauchy Problem for the Maxwell-Schrödinger System with a Power-Type Nonlinearity
1 Introduction2 Proof of Theorem1; 3 Global Existence; 4 Quantum Magnetohydrodynamics; References; Construction and Approximation of the Polyatomic Bitemperature Euler System; 1 Introduction; 2 The Mathematical Models; 2.1 The Bitemperature Euler System; 2.2 The Kinetic Model; 3 Construction of the Fluid Model; 3.1 Scaling on the One Dimensional BGK Model; 3.2 Hydrodynamic Limit; 4 Numerical Approximation; 4.1 Derivation of the Numerical Scheme; 4.2 Numerical Results; References; An Implicit-Explicit Scheme Accurate at Low Mach Numbers for the Wave Equation System; 1 Introduction
2 Low Mach Number Limit of the Wave Equation3 An IMEX Scheme Accurate at Low Mach Number; 3.1 Time Discretisation; 3.2 Space Discretisation; 4 L2-Stability Analysis; 5 Numerical Test Problems; 5.1 Order of Convergence and Accuracy; 5.2 Asymptotic Preserving Property; 6 Conclusions; References; Bose-Einstein Condensation and Global Dynamics of Solutions to a Hyperbolic Kompaneets Equation; 1 Introduction; 2 Definitions and Main Results; 3 Contraction; 4 Regularity and Compactness; 5 Proof of the Main Theorem; 6 Future Directions; References
2 Physical and Mathematical Models2.1 Mathematical Analysis; 3 Numerical Experiments; 4 Concluding Remarks; References; Optimal Control of Level Sets Generated by the Normal Flow Equation; 1 Introduction; 2 Optimal Control of Level Set Dynamics; 3 Approximate Solutions with the Extended Ritz Method; 4 Adjoint Equation and Optimization Procedure; 5 Simulation Results; 6 Conclusions; References; Emergent Dynamics for the Kinetic Kuramoto Equation; 1 Introduction; 1.1 The Kuramoto Model for N Oscillators; 1.2 The Kinetic Kuramoto Equation; 2 BV Solutions and the Front-Tracking Algorithm
2.1 Identical Oscillators2.2 Nonidentical Oscillators; 3 Phase Concentration of the Kuramoto-Sakaguchi Equation; 3.1 Identical Oscillators; 3.2 Nonidentical Oscillators; References; A Hyperbolic Model of Nonequilibrium Phase Change at a Sharp Liquid-Vapor Interface; 1 Context; 2 Mathematical Model; 2.1 Conservation Equations; 2.2 Hyperbolicity; 2.3 Comparison with Other Models; 2.4 Limitation; 3 Discretization and Test Cases; 3.1 Discretization Strategy; 3.2 Numerical Results; 4 Conclusion; References; The Cauchy Problem for the Maxwell-Schrödinger System with a Power-Type Nonlinearity
1 Introduction2 Proof of Theorem1; 3 Global Existence; 4 Quantum Magnetohydrodynamics; References; Construction and Approximation of the Polyatomic Bitemperature Euler System; 1 Introduction; 2 The Mathematical Models; 2.1 The Bitemperature Euler System; 2.2 The Kinetic Model; 3 Construction of the Fluid Model; 3.1 Scaling on the One Dimensional BGK Model; 3.2 Hydrodynamic Limit; 4 Numerical Approximation; 4.1 Derivation of the Numerical Scheme; 4.2 Numerical Results; References; An Implicit-Explicit Scheme Accurate at Low Mach Numbers for the Wave Equation System; 1 Introduction
2 Low Mach Number Limit of the Wave Equation3 An IMEX Scheme Accurate at Low Mach Number; 3.1 Time Discretisation; 3.2 Space Discretisation; 4 L2-Stability Analysis; 5 Numerical Test Problems; 5.1 Order of Convergence and Accuracy; 5.2 Asymptotic Preserving Property; 6 Conclusions; References; Bose-Einstein Condensation and Global Dynamics of Solutions to a Hyperbolic Kompaneets Equation; 1 Introduction; 2 Definitions and Main Results; 3 Contraction; 4 Regularity and Compactness; 5 Proof of the Main Theorem; 6 Future Directions; References