code class$=$"asciimath"$>(20$ points$)$ Show that there exists no solution uinC$^(\backslash$infty $)($R$+\backslash$times R$),$ periodic in x with period $1$ to del$\_($t$)$u$-$del$\_($x$)^(2)$u$=$u$^(2)$ such that u$(0,$x$)>1$ for any xinR. Hint: compare u with the solution v of del$\_($t$)$v$=($v$^(2))/(2)$ with initial data v$(0,$x$)=1.$