Theory, Numerics and Applications of Hyperbolic Problems I

1. Front Matter

   Pages i-xv

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2. The Sharp-Interface Limit for the Navier–Stokes–Korteweg Equations

   • Helmut Abels, Johannes Daube, Christiane Kraus, Dietmar Kröner

   Pages 1-13

3. Asymptotic Behavior of a Solution of Relaxation System for Flow in Porous Media

   • E. Abreu, A. Bustos, W. J. Lambert

   Pages 15-28

4. Optimal Control of Level Sets Generated by the Normal Flow Equation

   • Angelo Alessandri, Patrizia Bagnerini, Roberto Cianci, Mauro Gaggero

   Pages 29-41

5. Emergent Dynamics for the Kinetic Kuramoto Equation

   • Debora Amadori, Jinyeong Park

   Pages 43-58

6. A Hyperbolic Model of Nonequilibrium Phase Change at a Sharp Liquid–Vapor Interface

   • Matthieu Ancellin, Laurent Brosset, Jean-Michel Ghidaglia

   Pages 59-69

7. The Cauchy Problem for the Maxwell–Schrödinger System with a Power-Type Nonlinearity

   • Paolo Antonelli, Michele D’Amico, Pierangelo Marcati

   Pages 71-83

8. Construction and Approximation of the Polyatomic Bitemperature Euler System

   • Denise Aregba-Driollet, Stéphane Brull

   Pages 85-96

9. An Implicit–Explicit Scheme Accurate at Low Mach Numbers for the Wave Equation System

   • K. R. Arun, A. J. Das Gupta, S. Samantaray

   Pages 97-109

10. Bose–Einstein Condensation and Global Dynamics of Solutions to a Hyperbolic Kompaneets Equation

    • Joshua Ballew

    Pages 111-123

11. Finite Volume Methods for Hyperbolic Partial Differential Equations with Spatial Noise

    • Andrea Barth, Ilja Kröker

    Pages 125-135

12. A Hyperbolic Approach for Dissipative Magnetohydrodynamics

    • Hubert Baty, Hiroaki Nishikawa

    Pages 137-149

13. A General Well-Balanced Finite Volume Scheme for Euler Equations with Gravity

    • Jonas P. Berberich, Praveen Chandrashekar, Christian Klingenberg

    Pages 151-163

14. A Second-Order Well-Balanced Scheme for the Shallow Water Equations with Topography

    • Christophe Berthon, Raphaël Loubère, Victor Michel-Dansac

    Pages 165-177

15. A Lagrangian Approach to Scalar Conservation Laws

    • Stefano Bianchini, Elio Marconi

    Pages 179-190

16. On Uniqueness of Weak Solutions to Transport Equation with Non-smooth Velocity Field

    • Paolo Bonicatto

    Pages 191-203

17. Johnson–Segalman–Saint-Venant Equations for a 1D Viscoelastic Shallow Flow in Pure Elastic Limit

    • Sébastien Boyaval

    Pages 205-213

18. On the Exact Dimensional Splitting for a Scalar Quasilinear Hyperbolic Conservation Law

    • Michael D. Bragin, Boris V. Rogov

    Pages 215-225

19. On the Derivation of Newtonian Gravitation from the Brownian Agitation of a Regular Lattice

    • Yann Brenier

    Pages 227-235

20. Traffic Flow Models on a Network of Roads

    • Alberto Bressan

    Pages 237-248

The first of two volumes, this edited proceedings book features research presented at the XVI International Conference on Hyperbolic Problems held in Aachen, Germany in summer 2016. It focuses on the theoretical, applied, and computational aspects of hyperbolic partial differential equations (systems of hyperbolic conservation laws, wave equations, etc.) and of related mathematical models (PDEs of mixed type, kinetic equations, nonlocal or/and discrete models) found in the field of applied sciences.

• Hyperbolic Conservation Laws
• Kinetic Equations
• Non-linear Conservation
• Multi-phase Flow
• Navier-Stokes Equations
• partial differential equations

• Department of Mathematics, Würzburg University, Würzburg, Germany

  Christian Klingenberg

• Department of Mathematics, RWTH Aachen University, Aachen, Germany

  Michael Westdickenberg

Christian Klingenberg is a professor in the Department of Mathematics at Wuerzburg University, Germany. 

Michael Westdickenberg is a professor at the Institute for Mathematics at RWTH Aachen University, Germany.

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