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涵盖了一些高级主题在线性和非线性偏微分方程。主题包括伪微分算子和椭圆规律;元素的微局部分析;奇点的传播;椭圆算子谱理论;变分原理;量子力学中的薛定谔方程及其含义;抛物方程和他们的角色在扩散过程;双曲型方程和波传播;双曲型方程的柯西问题; elements of scattering theory; nonlinear elliptic equations in Riemannian geometry, including the Yamabe problem, prescribed scalar curvature problem, and Einstein-Kähler metrics; the Navier-Stokes equations in hydrodynamics; simplest properties and open problems in nonlinear hyperbolic equations and shock waves; the Korteweg-de Vries equation and its relation to inverse scattering problems; solitons and algebro-geometric solutions.

先决条件:数学5101最低等级的C -