Let u be the unique solution of
∂u∂t=∂2u∂x2 where (x,t)∈(0,1)×(0,∞)u(x,0)=sinπx,x∈(0,1)u(0,t)=u(1,t)=0,t∈(0,∞)}
Then which of the following is true?
1. There exists (x,t)∈(0,1)×(0,∞) such that u(x,t)=0
2. There exists (x,t)∈(0,1)×(0,∞) such that ∂u∂t(x,t)=0
3. The function etu(x,t) is bounded for (x,t)∈(0,1)×(0,∞)
4. There exists (x,t)∈(0,1)×(0,∞) such that u(x,t)>1