Help me with this one please.

Consider the initial value problem
\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}),<br /> \frac{\partial u}{\partial x_{2}}(x_{1},0)=\varphi _{1}(x_{1})<br />

where a is a real number.


1)For which class of initial data can one solve the problem?
2)Is this problem well-posed? If not, what goes wrong?
3)Do the answers to 1) and 2) depend on a?