Nonlinear Hyperbolic Problems: Theoretical, Applied, and Computational Aspects

This book contains original papers presented at the Fourth International Conference on Hyperbolic Problems which was held on April 3-8, 1992 in Taormina (Sicily), Italy. The aim of the Conferences in this cycle is to bring together scientists with interest in theo­ retical, applied and computational aspects of hyperbolic partial differential equations. The contributions, well balanced among these three aspects, deal with: mathematical theory of wave propagation, kinetic theory, existence, uniqueness and stabil­ ity of solutions, mathematical modeling of physical phenomena, stability and convergence of numerical schemes, multidimensional computational applications, etc. The papers are printed in the authors' alphabetic order following the idea both of mixing together topics of interest to different areas and of considering either theoretical results connected with applied problems or new applications with an essential mathemat­ ical approach. The Proceedings from the previous Conferences held in St. Etienne (1986), Aachen (1988) and Uppsala (1990) appeared respectively as: • Lecture Notes in Mathematics, 1270, P. Carasso, P. A. Raviart & D. Serre (Eds.), Springer-Verlag (1987) • Notes on Numerical Fluid Mechanics, 24, J. Ballmann & R. Jeltsch (Eds.), Vieweg (1989 ) • Third International Conference on Hyperbolic Problems, B. Engquist & B. Gustafs­ son (Eds.), Vol. I, II, Studentlitteratur, Uppsala University (1991). The organizers and the editors of the Conference would like to thank the Scientific Committee for the generous support, for suggesting the invited lectures, and for selecting the contributed papers.

On spurious difference solutions of discretizations of nonlinear hyperbolic differential equations.- Symmetry analysis for waves in hole enlargement.- Flux formulation using a fully 2D approximate Roe Riemann solver.- Extended thermodynamics of charge carrier transport in semiconductors.- Resonances of Schwarzschild black holes.- Well-posedness of nonlinear hyperbolic problems and the dynamics of compressible fluids.- Numerical viscosity, entropy condition and convergence of finite volume schemes for general multidimensional conservation laws.- Existence of solutions for a class of hyperbolic systems of p conservation laws (p > 3).- Direct solution of two-dimensional scalar conservation laws with Riemann initial data by the GSC method.- A practical hyperbolic problem: the unsteady gas-liquid flow in a pipe.- Stability of shock waves of 3×3 model MHD equations.- Numerical simulation of high frequency scattering waves using exact controllability methods.- Discrete Boltzmann equation with multiple collisions.- The Burgers equation: explicit solutions of an initial boundary value problem.- Hyperbolic problems in kinetic theory.- Convergence of an explicit upwind Van Leer scheme on a triangular mesh for hyperbolic equations.- Large time, weak solutions to reacting Euler equations.- Classes of exact solutions for the discrete Boltzmann models.- On a class of large time-step schemes for conservation laws.- A numerical technique to compute Euler flows at impermeable boundaries based on physical considerations.- Equivalence of referential and spatial field equations in continuum physics.- Weak solutions in rate type dynamic viscoplasticity.- Improved residual smoothing.- Second order evolution equations and progressive waves.- Parallel computer solution of the wave equation.- Numerical solution of a moving boundary hyperbolic problem.- A new multidimensional Euler-scheme.- The influence of a source term, an example: chemically reacting hypersonic flow.- Implicit schemes for P-system equations via Roe’s linearisation.- A reduction approach for determining exact solutions to a hyperbolic nonautonomous model.- Spectral element-FCT method for the compressible Euler equations.- Multi-dimensional Riemann problems for linear hyperbolic systems: Part I.- Multi-dimensional Riemann problems for linear hyperbolic systems: Part II.- A theory of fluid mixing.- Simple Godunov-Type schemes for Lagrangian gas dynamics.- A modified GMRES method for steady state solutions of hyperbolic systems.- Absorbing boundary conditions for Maxwell’s equations.- Shock wave analysis for hyperbolic systems of conservation laws having spatial variability.- A mathematical model of traffic flow on a network of roads.- A generalized lagrangian method for solving the Euler equations.- Parameter identification for a hyperbolic equation modelling chromatography.- Weak discontinuity interaction with shocks and the reductive perturbation method with positive and negative nonlinearity.- Improvements of upwind formulations on unstructured meshes.- Regularity of a scalar Riemann problem in two space dimensions.- Convergence to steady state of solutions of viscous conservation laws.- A conservative front tracking scheme for 1D hyperbolic conservation laws.- Multi-dimensional numerical schemes.- A linear hyperbolic system with stiff source terms.- Energy propagation in linear hyperbolic systems in the presence of dissipation.- Nonlinear evolution of an obliquely propagating hydromagnetic wave.- Two-dimensional boundary layer equations: high resolution capturing methods.- Characteristic Galerkin methods for hyperbolic problems.- The symmetric hyperbolic equations of extended thermodynamics.- Non linear Klein-Gordon equation in Schwarzschild-like metrics.- Galilean quasilinear systems of PDE’s and the substitution principle.- Some asymptotic results concerning a hyperbolic mixed problem in viscoelasticity.- Waves in media with periodic fine structure.- On some exact solutions of hyperbolic Boussinesq equation with dissipation.- Convergence of approximate solutions of the Cauchy problem for a 2×2 nonstrictly hyperbolic system of conservation laws.- Universal principles for balance law systems.- Implicit numerical methods for kinetic equations.- Travelling wave solutions of convection-diffusion systems and nonconservative hyperbolic systems.- The Riemann problem for two-dimensional gas dynamics.- Flux-vector splitting for compressible low Mach number flow.- Application of an E.N.O. scheme to simulate the ion etching process.- Entropy dissipation in finite difference schemes.- The resolution of compressible flow fields by adaptive finite volume methods.- Hyperbolic conservation laws, finite difference schemes and error estimates.- Numerical simulation of high speed reactive flows with adaptive mesh refinement.- A model for pipeline three-phase flows.- The compactness of front-tracking for chromatography electrophoresis and incompressible multiphase flow.- Singular perturbations of first-order hyperbolic systems.- List of Participants.- Conference data.