Let $u$ be the unique solution of
$$\left.\begin{array}{lr}\dfrac{\partial u}{\partial t}=\dfrac{\partial^{2} u}{\partial x^{2}} \text { where }(x, t) \in(0,1) \times(0, \infty) \\ u(x, 0)=\sin \pi x, & x \in(0,1) \\ u(0, t)=u(1, t)=0, & t \in(0, \infty)\end{array}\right\}$$
Then which of the following is true?
1. There exists $(x, t) \in(0,1) \times(0, \infty)$ such that $u(x, t)=0$
2. There exists $(x, t) \in(0,1) \times(0, \infty)$ such that $\frac{\partial u}{\partial t}(x, t)=0$
3. The function $e^{t} u(x, t)$ is bounded for $(x, t) \in(0,1) \times(0, \infty)$
4. There exists $(x, t) \in(0,1) \times(0, \infty)$ such that $u(x, t)>1$