Discontinuous Solutions to Nonlinear Evolutionary Partial Differential Equations

Authors: Gui-Qiang Chen

Title: Discontinuous Solutions to Nonlinear Evolutionary Partial Differential Equations

Abstract
We analyze some recent developments in studying discontinuous solutions to nonlinear evolutionary partial differential equations. The central problems include the existence, compactness, and large-time behavior of discontinuous solutions. The nonlinear equations we discuss include nonlinear hyperbolic systems of conservation laws (especially the compressible Euler equations) and the compressible Navier-Stokes equations. Some of recent ideas, approaches, and methods are also discussed.

This article has appeared in:
AMS/IP Studies in Advanced Mathematics 20 , pages 443-454 (2000) , Proceedings of International Congress of Chinese Mathematicians (Beijing, December 1998)

This paper is available in the following formats:

A closely related paper is Decay of Entropy Solutions of Nonlinear Conservation Laws.

Another closely related paper is Compressible Euler Equations with a General Pressure Law .

Author Address
    Gui-Qiang Chen
    Department of Mathematics
    Northwestern University
    Evanston, IL 60208-2730
    gqchen@math.nwu.edu