Nonlinear Wave Equations
نویسنده
چکیده
This paper explores the properties of nonlinear wave equations. The proof for the existence and uniqueness of solutions to the 1+1 dimensional linear wave equation with smooth data is given. The D’Alembert formula is then presented in its full generality for the nonlinear equation. Important properties like the domain of dependence and propagation of information are discussed and motivated. These are used to address subtle questions concerning local existence of the nonlinear wave equation. Finally, global and long-time properties are considered, showcasing the utility of energy estimates as well as geometric arguments in higher dimensions.
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