Let $u(x, t)$ be the solution of the initial boundary value problem
$$ \begin{array}{c}
\frac{\partial u}{\partial t}-\frac{\partial^{2} u}{\partial x^{2}}-u=0, \quad 0< x < \pi, t>0, \\
u(x, 0)=2 \sin \left(\frac{3 x}{2}\right) \cos \left(\frac{x}{2}\right), \quad 0<x<\pi, \\ u(0, t)=u(\pi, t)=0, \quad t>0. \end{array}$$
Then the value of $\displaystyle \lim _{ t \rightarrow \infty} u\left(\frac{3 \pi}{4}, t\right)$ is equal to (rounded off to two decimal places) $\_\_\_\_\_\_\_\_$
