Hyperbolic Problems

Theory, Numerics and Applications(In 2 Volumes)

This two-volume book is devoted to mathematical theory, numerics and applications of hyperbolic problems. Hyperbolic problems have not only a long history but also extremely rich physical background. The development is highly stimulated by their applications to Physics, Biology, and Engineering Sciences; in particular, by the design of effective numerical algorithms. Due to recent rapid development of computers, more and more scientists use hyperbolic partial differential equations and related evolutionary equations as basic tools when proposing new mathematical models of various phenomena and related numerical algorithms.

This book contains 80 original research and review papers which are written by leading researchers and promising young scientists, which cover a diverse range of multi-disciplinary topics addressing theoretical, modeling and computational issues arising under the umbrella of “Hyperbolic Partial Differential Equations”. It is aimed at mathematicians, researchers in applied sciences and graduate students.

Contents:

• Volume 1:

  • SBV Regularity for Scalar Conservation Laws (Stefano Bianchini)
  • Stellar Structure, Dynamics and Stability (Tao Luo and Joel Smoller)
  • Irrotational Flows for Chaplygin Gas: Conical Waves (Denis Serre)
  • Existence of Algebraic Vortex Spirals (Volker Elling)
  • Darcy's Law in One-Dimensional Isentropic Porous Medium Flow (Ronghua Pan)
  • A Nonlocal Conservation Law from a Model of Granular Flow (Debora Amadori and Wen Shen)
  • A Simple Model for Cavitation with Non-condensable Gases (Mathieu Bachmann, Siegfried Müller, Philippe Helluy and Hélène Mathis)
  • CDG Method for Navier–Stokes Equations (Slavko Brdar, Andreas Dedner and Robert Klöfkorn)
  • and other papers

• Volume 2:

  • Stable Numerical Scheme for the Magnetic Induction Equation with Hall Effect (Paolo Corti)
  • On the Space-Time Expansion Discontinuous Galerkin Method (P Engel and C Rohde)
  • Sharp Interface Limits for Korteweg Models (Jan Giesselmann)
  • Finite Volume Methods for the Two-fluid MHD Equations (Harish Kumar)
  • Asymptotic Stability of Rarefaction Waves in Radiative Hydrodynamics (Chunjin Lin)
  • Adaptive Grids and the Entropy Error Indicator (G Puppo and M Semplice)
  • Mechanism of Singularity Formation for Linearly Degenerate Quasilinear Hyperbolic Systems (Peng Qu)
  • Layered Structures: Instability of the Shock Waves and Electrodynamical Instability (Roman Semenko)
  • Dispersive Limits of the Nonlinear Klein–Gordon Equation (Kung-Chien Wu and Chi-Kun Lin)
  • A Result on Global Solutions to 3D Complex Ginzburg–Landau Equation (Penghong Zhong, Shu Wang, Ke Wang and Ronghui Yang)
  • and other papers