# [Differential Equations I] A Report on Differential Equations I

[Differential Equations I] A Report on Differential Equations I This file provides the solution for the exercises given in the class. Exercise 1 gives an elementary proof of the Sobolev inequality. Exercise 2 and Exercise 3 introduce a basic energy … Continue reading

# [Differential Equations II] Final Report

In this report, we study the global existence of solutions to nonlinear dispersive wave equations \begin{eqnarray*}\partial_t^2 u + \frac{1}{\rho^2} |\partial_x|^{2\rho} u &=& \lambda |\partial_t u |^{p-1} \partial_t u\end{eqnarray*} in one space dimension where $0 < \rho \leqslant 2$, \$\rho \neq … Continue reading