# Initial value problem

• Feb 16th 2011, 09:03 AM
sinichko
Initial value problem
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}),
\frac{\partial u}{\partial x_{2}}(x_{1},0)=\varphi _{1}(x_{1})
$

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 $a$?