Partial Differential Equations/The wave equation

Fundamental solution

Initial value problem

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

Exercises

Sources

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