Question

$u^{2}_{x}/2−u_{y} = −x^{2}/2
;\\
u(x, 0) = x$
How do we show that that the solution blows up in finite time and explain this in
terms of characteristic of the equation.

Answer 1

hmm, that equation is difficult to read

Answer 2

\[\begin{gathered}
u_x^2/2 - {u_y} = - {x^2}/2; \hfill \\
u(x,0) = x \hfill \\
\end{gathered} \]

I have rewrote them @perl