\(\displaystyle \frac{\partial^2 u}{\partial x^2} = \frac{\partial^2 u}{\partial t^2} \qquad (t \geq 0, x \geq 0) \)

\(\displaystyle \frac{\partial u(0,t)}{\partial t} = \alpha \frac{\partial u(0,t)}{\partial x} \qquad (t \geq 0) \)

\(\displaystyle u(x,0) = \phi_0 (x) \qquad (x \geq 0) \)

\(\displaystyle \frac{\partial u}{\partial t} (x, 0) = \phi_1 (x) \qquad (x \geq 0) \)

where \(\displaystyle \alpha \neq -1 \) is a constant and \(\displaystyle \phi_0 (x) \) and \(\displaystyle \phi_1 (x) \) are twice continuously differentiable for \(\displaystyle x > 0 \) and vanish near \(\displaystyle x = 0 \). Show that in general no solution exists when \(\displaystyle \alpha = -1 \).