Mathematics Colloquia and Seminars

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Description

This talk is an expository lecture on the well-posedness problem of nonlinear wave equations. First we will give a review on some basic results and techniques for linear wave equations. Then we will see how to use energy estimates, Sobolev embedding and some simple interpolation inequalities to derive some classical local and global existence results for nonlinear wave equations. We will also talk about some more recent results and open problems on global existence and minimal regularity solutions of nonlinear wave equations. The lecture will be self-contained and no previous background in PDE is required.