(1) Department of Mathematics, Northwestern University, 2033 Sheridan Road, Evanston, Illinois 60208-2730, USA
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 parabolichyperbolic 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.Dedicated to IMPA on the occasion of its 50th anniversary