
Initial value problem
Help me with this one please.
Consider the initial value problem
$\displaystyle \frac{\partial ^{2}u}{\partial x_{2}^{2}}+a\frac{\partial ^{2}u}{\partial x_{1}^{2}} =0, u(x_{1},0)=\varphi _{0}(x_{1}),
\frac{\partial u}{\partial x_{2}}(x_{1},0)=\varphi _{1}(x_{1})
$
where $\displaystyle a$ is a real number.
1)For which class of initial data can one solve the problem?
2)Is this problem wellposed? If not, what goes wrong?
3)Do the answers to 1) and 2) depend on $\displaystyle a$?