# Questions tagged [wave-equation]

The wave-equation tag has no usage guidance.

3
questions

**4**

votes

**1**answer

813 views

### Finite speed propagation by finite energy method

I am currently investigating some finite speed propagation property for nonlinear wave equations, and I am asking myself if there is a way of proving such a property just using energy estimates like ...

**2**

votes

**0**answers

84 views

### Inhomogeneous wave equation - a reference

Consider the inhomogeneous wave equation
$$\frac{\partial^2u}{\partial t^2}-\Delta u=\rho(x,t),$$
where $x=(x_1,\dots,x_n)$, $\Delta=\sum_{i=1}^n\frac{\partial^2}{\partial x_i^2}$ is the Laplacian, $\...

**1**

vote

**3**answers

616 views

### Uniqueness of solution of the wave equation

Consider the wave equation
$$\frac{\partial^2 u}{\partial t^2}-\sum_{i=1}^n\frac{\partial^2 u}{\partial x_i^2}=0$$
with initial conditions
$$u|_{t=0}=\frac{\partial u}{\partial t}|_{t=0}=0$$
Does ...