Some Recent Methods for Partial Differential Equations of Divergence Form

Authors: Gui-Qiang Chen

Title: Some Recent Methods for Partial Differential Equations of Divergence Form

Abstract
Some recent methods for solving second-order nonlinear partial differential equations of divergence form and related nonlinear problems are surveyed. These methods include entropy methods via the theory of divergence-measure fields for hyperbolic conservation laws, kinetic methods via kinetic formulations for degenerate parabolic-hyperbolic equations, and free-boundary methods via free-boundary iterations for multidimensional transonic shocks for nonlinear equation of mixed elliptic-hyperbolic type. Some recent trends in this direction are also discussed.
This article has appeared in:
Boletim da Sociedade Brasileira de Matem\'{a}tica (Bol. Soc. Bras. Math.) vol. 34 (1), pages 107-144, 2003
This paper is available in the following formats:
A closely related paper is change me. 
Author Address
    Gui-Qiang Chen
    Department of Mathematics
    Northwestern University
    Evanston, IL 60208-2730
    USA
    gqchen@math.northwestern.edu