Preprint 2003-001

Some Recent Methods for Partial Differential Equations of Divergence Form

Gui-Qiang Chen

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.

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Gui-Qiang Chen, <>
Publishing information:
Dedicado ao IMPA na ocasi\~ao de seu 50${}^o$ anivers\'ario, In: Boletim Da Sociedade Brasileira De Matem\'{a}tica, 2003
Submitted by:
<> January 1 2003.

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