Partial Differential Equations | ||

← The Fourier transform | The wave equation |
The Malgrange-Ehrenpreis theorem → |

**Definition 9.?**:

Let $f,g\in {\mathcal {C}}(\mathbb {R} ^{d})$ . The **initial value problem for the wave equation** is defined to be the problem to find a function $u:\mathbb {R} ^{d}\to \mathbb {R}$ such that

- ${\begin{cases}\end{cases}}$ .

We will first solve the initial value problem in the case

Partial Differential Equations | ||

← The Fourier transform | The wave equation |
The Malgrange-Ehrenpreis theorem → |