## Partial differential equations in ChinaIn the past few years there has been a fruitful exchange of expertise on the subject of partial differential equations (PDEs) between mathematicians from the People's Republic of China and the rest of the world. The goal of this collection of papers is to summarize and introduce the historical progress of the development of PDEs in China from the 1950s to the 1980s. The results presented here were mainly published before the 1980s, but, having been printed in the Chinese language, have not reached the wider audience they deserve. Topics covered include, among others, nonlinear hyperbolic equations, nonlinear elliptic equations, nonlinear parabolic equations, mixed equations, free boundary problems, minimal surfaces in Riemannian manifolds, microlocal analysis and solitons. For mathematicians and physicists interested in the historical development of PDEs in the People's Republic of China. |

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### Contents

Nonlinear Hyperbolic Conservation Laws | 19 |

Viscosity Solutions of Fully Nonlinear Elliptic and Parabolic | 42 |

Free Boundary Problems | 67 |

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Acta Math admits a unique boundary conditions boundary value problem Cauchy problem centered wave characteristic Chen classical solution coefficients conservation laws consider constant contact discontinuity convex corresponding degenerate elliptic equations degenerate parabolic equations denotes derivatives Diff dimensional Dirichlet problem elliptic equations elliptic systems equa Equations in China estimates existence and uniqueness ferromagnetic ferromagnetic chain free boundary problem Fudan fully nonlinear global solution Guo Boling initial data initial value problem Korteweg-de Vries Korteweg-der Vries equation linear matrix method microlocal analysis minimal surfaces mixed equations nonlinear obtained parabolic equations partial differential equations problem for quasilinear problem for system proved the existence quasilinear degenerate quasilinear hyperbolic systems Riemann problem 1.1 satisfies Scientia Sinica second order similarity solution singular solvability Stefan problem studied Suppose system of conservation system of ferromagnetic Ta-tsien Theorem theory tions unique global Univ variables viscosity solutions Wang weak solution