- The student understands the definition and classification of hyperbolic equations.
- The student is familiar with basic properties of linear wave equations.
- The student is aware of standard local/global existence results for semi- and quasilinear wave equations.
- The student can work with weak solutions.
- The student is able to use energy estimates, Fourier transform, Strichartz estimates etc.
Nonlinear wave equations are an important class of second-order partial differential equations. These equations occur in an abundance of problems in science and engineering. Wave equations are, in particular, indispensable for an understanding of physical phenomena such as acoustics, electromagnetics, fluid dynamics and general relativity. In this course we cover the basic tools and results for linear and nonlinear wave equations.|