Partial Differential Equations

This course will introduce the basic knowledge of Sobolev spaces used in Partial Differential Equations. Based on Sobolev spaces, the well-posedness problems such as existence, uniqueness and regularity for weak solutions of linear partial differential equations of second order will be investigated. These linear partial differential equations include linear elliptic partial differential equations, linear parabolic partial differential equations and linear hyperbolic partial differential equations. The aim is to help students understand the elementary theory and modern methods of linearpartial differential equations.